1.

If A (3, y) is equidistant from points P (8, -3) and Q (7,6) , find the value of y and find the distance AQ.

Answer»

Coordinates are P(8, -3) and Q(7,6) 

The point A (3, y) is equidistant. 

Using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

⇒ PA = QA

\(\sqrt{(3 - 8)^2 + (y + 3)^2}\) = \(\sqrt{(3 - 7)^2 + (y - 6)^2}\)

On squaring both sides, we get

(3 - 8)2 + (y + 3)2 = (3 - 7)2 + (y - 6)2

25 + y2 + 6y + 9 = 16 + y2 - 12y + 36

y = 1

AQ = \(\sqrt{(3 - 7)^2 + (1 - 6)^2}\) = \(\sqrt{16 + 25}\) = \(\sqrt{41}\) units



Discussion

No Comment Found

Related InterviewSolutions