CBSE Class 10-Mathematics: Chapter –7 Coordinate Geometry Part 9

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Question 20:

Find the ratio in which the line segment joining and is divided by the . Also find the coordinates of the point of division.

Answer:

Let the coordinates of point of division be and suppose it divides line segment joining and in .

According to Section formula, we get

Putting value of in , we get

Therefore, point on x–axis divides line segment joining and .

Question 21:

If are the vertices of a parallelogram taken in order, find and .

Answer:

Let and

We know that diagonals of parallelogram bisect each other. It means that coordinates of midpoint of diagonal AC would be same as coordinates of midpoint of diagonal BD. … (1)

Using Section formula, the coordinates of midpoint of are:

Using Section formula, the coordinates of midpoint of BD are:

According to condition (1), we have

⇒ x=6

Again, according to condition (1), we also have

Therefore, and

Question 22:

Find the coordinates of a point A, where AB is the diameter of a circle whose center is and B is .

Answer:

We want to find coordinates of point A. AB is the diameter and coordinates of center are and, coordinates of point B are .

Let coordinates of point A are .

Using section formula, we get

Therefore, Coordinates of point A are .