CBSE Class 10-Mathematics: Chapter –7 Coordinate Geometry Part 16
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Question 21:
We know that median of a triangle divides it into two triangles of equal areas. Verify this result for whose vertices are and .

Two Triangles of Equal Areas
Answer:
We have whose vertices are given.
We need to show .
Let coordinates of point
Using section formula to find coordinates of , we get
Therefore, coordinates of point are
Using formula to find area of triangle:
Area of
Area cannot be in negative.
Therefore, we just consider its numerical value.
Therefore, area of
Again, using formula to find area of triangle:
Area of
From (1) and (2), we
Hence Proved
Question 22:
Find the center of a circle passing through the points .

Find the Centre of a Circle
Answer:
Let , be the center of the circle passing through the points A and .
Then .
Taking AP = BP
Again, taking
Putting the value of in eq. (i)
Hence, the center of the circle is