CBSE Class 10-Mathematics: Chapter –7 Coordinate Geometry Part 11

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Question 3:

Find the centroid of the triangle whose vertices are and .

Answer:

Let be the coordinate of centroid

Coordinate of centroid is

Question 4:

Prove that in a right-angled triangle, the mid-point of the hypotenuse is equidistant from the vertices.

Maths-Class-10-Marks3-Che-7-Ques-4

The Hypotenuse is Equidistant from the Vertices

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Answer:

Let are the vertices of right-angled triangle

Coordinate of

i.e.

Hence, is Equidistant from the vertices.

Question 5:

Prove that diagonals of a rectangle bisect each other and are equal.

Answer:

Let ABCD be a rectangle take A as origin the vertices of a rectangle are

Maths-Class-10-Marks3-Che-7-Ques-5-The Vertices of a Rectang …

The Vertices of a Rectangle

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Mid-point of

Mid-point of

Mid-point of Mid-point of

Hence proved

Question 6:

The line joining the points is bisected at P. If P lies on the line find the value of .

Maths-Class-10-Marks3-Che-7-Ques-6-Find the value of k

Find the Value of K

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Answer:

Coordinate of

P lies on equation