# CBSE Class 10-Mathematics: Chapter – 7 Coordinate Geometry Part 22 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 14**:

The area of a triangle is . Two of its vertices are . The third vertex lies on . Find the third vertex.

**Answer**:

Let the third vertex be , Other two vertices of the are and

lies on eq.

On solving eq.

We get

Similarly, on solving eq.

We get

**Question 15**:

Prove that the point are collinear, if

**Answer**:

Since are collinear

Area

Dividing by

**Question 16**:

If, is equidistant from and , find the values of x. Also, find the distances QR and PR.

**Answer**:

It is given that Q is equidistant from P and R. Using Distance Formula, we get

Squaring both sides, we get

Thus, Q is or .

Using Distance Formula to find QR, we get

Using value of

Therefore,

Using Distance Formula to find , we get

Using value of

Using value of

Therefore,