In a plane rectangular coordinate system points LMN and O are represented by the coordinates 501105 and 15 respectively Consider a variable point P in the same plane The minimum value of PLPMPNPO is

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

If the distance between the points

(2, 3)

and

(a, 0)

is

3

, then

a =

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

The distance between the points

(a \cos θ + b \sin θ, 0)

and

(0, a \sin θ - b \cos θ)

, is

MEDIUM

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

The point

(x, y)

is equidistant from the points

(7, 1)

and

(3, 5)

, Then

MEDIUM

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

The points

(k - 1, k + 2), (k, k + 1), (k + 1, k)

are collinear for

MEDIUM

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

Let

A B C D

be a square of side length

1

, and

Γ

a circle passing through

B

and

C

, and touching

A D

. The radius of

Γ

is

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

If the three points

A (1, 6), B (3, - 4)

and

C (x, y)

are collinear then the equation satisfying by

x

and

y

is

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

The distance between the points $(0, 0)$ and $(- 8, 6)$ is

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

The distance of a point

(3, 4)

from the origin is _____ units.

HARD

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

If the distance between the points

(x, 0)

and

(- 7, 0)

is

10

. Then, the possible values of

x

are ______.

MEDIUM

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

Let

x_{0}, y_{0}

be fixed real numbers such that

x_{0}^{2} + y_{0}^{2} > 1

. If

x, y

are arbitrary real numbers such that

x^{2} + y^{2} \leq 1,

then the minimum value of

{(x - x_{0})}^{2} + {(y - y_{0})}^{2}

is

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

The distance between the co-ordinates of a point

(p, q)

from the origin is

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

If

(x, y)

is equidistant from

(a + b, b - a)

and

(a - b, a + b)

,

then

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

The distance between two points

(3, 5)

and

(5, 7)

will be

MEDIUM

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

A (0, 0)

,

B (3, 0)

,

C (3, 4)

are the vertices of _____ triangle.

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

If the distance between the points $A (2, - 3)$ and $B (2, a)$ is $5$ , then the negative value of $a$ is

HARD

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

Quadrilateral formed by the vertices

(1, 4), (- 5, 4), (- 5, - 3)

and

(1, - 3)

will be

MEDIUM

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

Let

A (- 5, 5), B (4, - 5) and C (4, 5)

be the vertices of the triangle

A B C .

If a circle passes through the vertices of

△ A B C

then the area (in sq. units) lying inside the circle but outside the

△ A B C

is

EASY

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

A B C

is an isoceless triangle. If the coordinates of the base are

B (1, 3), C (- 2, 7),

the coordinates of

A

are

HARD

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

Let

A B C D

be a square of side length

1 .

Let

P, Q, R, S

be points in the interiors of the sides

A D, B C, A B, C D

respectively, such that

P Q

and

R S

intersect at right angles. If

P Q = \frac{3 \sqrt{3}}{4},

then

R S

equals

MEDIUM

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

Let

A = (a_{1}, a_{2})

and

B = (b_{1}, b_{2})

be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between

A

and

B

?

In a plane rectangular coordinate system, points $L, M, N$ and $O$ are represented by the coordinates $(- 5, 0), (1, - 1), (0, 5)$ , and $(- 1, 5)$ respectively. Consider a variable point $P$ in the same plane. The minimum value of $PL + PM + PN + PO$ is

Important Questions on Congruence

Learn and Prepare for any exam you want !

In a plane rectangular coordinate system, points L, M, N and O are represented by the coordinates (-5,0),(1,-1),(0,5), and (-1,5) respectively. Consider a variable point P in the same plane. The minimum value of PL+PM+PN+PO is

Important Questions on Congruence

Learn and Prepare for any exam you want !

In a plane rectangular coordinate system, points $L, M, N$ and $O$ are represented by the coordinates $(- 5, 0), (1, - 1), (0, 5)$ , and $(- 1, 5)$ respectively. Consider a variable point $P$ in the same plane. The minimum value of $PL + PM + PN + PO$ is