CBSE Class 10-Mathematics: Chapter – 7 Coordinate Geometry Part 16 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 .

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 .

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