Question

The points P (-5,a) , Q (b,7) and R (1,-3) are collinear such that PQ= QR . Find the values of a and b

Answer 1

Here is the answer to your question.

It is given that PQ = QR.

⇒ PQ2 = QR2

⇒ (1 – 6)2 + (3 – 1)2 = (x – 1)2 + (8 – 3)2  [Distance formula]

⇒ 25 + 4= (x – 1)2 + 25

⇒ 4 = (x – 1)2

⇒ (x – 1) = 2 or –2

⇒ x = 3 or –1

 

Thus, the value of x is either 3 or –1

Answer 2

Since Q is the midpoint of PR. Apply midpoint theorem like this:b=−5+12,7=a+(−3)2