MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 20

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The three vertices of a parallelogram are $(3,4), (3,8) and (9,8)$ . Find the fourth vertex.

Important Questions on Co-Ordinate Geometry

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IMPORTANT

MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 21

Find a point which is equidistant from the points

A (- 5,4) and B (- 1,6)

. How many such points are there?

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MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 22

The centre of a circle is

(2 a, a - 7)

. Find the values of

a

, if the circle passes through the point

(11, - 9)

and has diameter

10 \sqrt{2}

units.

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MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 23

Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter's school and then reaches the office. What is the extra distance travelled by Ayush in reaching the office? (Assume that all distances covered are in straight lines). If the house is situated at

(2, 4)

, bank at

(5, 8)

, school at

(13, 14)

and office at

(13, 26)

and coordinates are in kilometers.

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MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 24

Find the value of

k

, if the point

P (0, 2)

is equidistant from

(3, k)

and

(k, 5)

.

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MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 25

If

(- 4,3)

and

(4,3)

are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior.

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MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 25

If

(- 4,3)

and

(4,3)

are two vertices of an equilateral triangle, if the coordinates of the third vertex, given that the origin lies in the exterior of the triangle is

(a, b + c \sqrt{3}) u n i t s

. Find the value of

c

.

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MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 26

Show that the points

(- 3, 2), (- 5, - 5), (2, - 3) and (4, 4)

are the vertices of a rhombus. Find the area of this rhombus.

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MATHEMATICS CLASS X>Chapter 6 - Co-Ordinate Geometry>EXERCISE 6.2>Q 27

Find the coordinates of the circumcenter of the triangle whose vertices are

(3,0), (- 1, - 6) and (4, - 1) .

Also, find its circumradius.