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
Using section formula, we get
Therefore, Coordinates of point A are .