All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 1

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Join two points $P (2, 2)$ and $Q (4, 2)$ in a plane. Fixed the point $P$ and rotate the line $P Q$ in an anti-clockwise direction at an angle of $270 °$ . Then, the new coordinates of point $Q$ and the area formed by this figure will be-

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Important Questions on Section and Mid-Point Formulae

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 2

If

G

be the centroid of a

△ A B C

and

P

be any other point in the plane, then

G A^{2} + G B^{2} + G C^{2} + 3 G P^{2}

is equal to

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 3

A figure is shown below

Question Image

If we rotate this graph about $O$ at an angle of $180 °$ in anticlockwise direction, then the intersection point of diagonals will be

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 4

If

(- 4, 3)

and

(4, 3)

are two vertices, of an equilateral triangle and the origin lies in the interior of the triangle, then the coordinates of the third vertex will be:

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 5

Suppose there are four points

A (2, 4), B (6, 4), C (6, 6) and D (2, 6)

which lie in the first quadrant. If we rotate only the axes at an angle of

90 °

in anticlockwise direction, then what will be the new coordinates of the point

C

and what will be the name of the figure, when we join adjacent points.

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 6

Suppose

P Q

be a pole, whose coordinates are

P (1, 3)

and

Q (3, 3)

and

A

be the position of a man whose coordinates are

(1, 1)

. If a pole makes an angle of elevation to the point

A

, then the angle

θ

is

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 6

Suppose

P Q

be a pole, whose coordinates are

P (1, 3)

and

Q (3, 3)

and

A

be the position of a man whose coordinates are

(1, 1)

. If we shift the origin at

(1, 1)

, then the angle

θ

is?

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 7

The sum of the squares of the distances of a moving point

(x, y)

from two fixed points

(a, 0)

and

(- a, 0)

is equal to a constant quantity

2 b^{2}

. The value of

x^{2} + y^{2} + a^{2}

is equal to

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All In One ICSE Mathematics Class 10>Chapter 11 - Section and Mid-Point Formulae>CHALLENGERS>Q 8

A point

(x, y)

moves, so that the sum of its distances from

(a e, 0)

and

(- a e, 0)

is

2 a

. If

b^{2} = a^{2} (1 - e^{2})

, then

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}

is equal to