Question

If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the value of x.

• A. x = 4
• B. x = -4
• C. x = 5
• D. x = -5

Answer 1

Answer: (A), (B)

The correct options are
A

x = 4

B

x = -4

Given P = (5, - 3), Q = (0, 1), R = (x, 6) and PQ = QR

$\because$ Distance between points $(x_1,y_1)$ and$(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

$\therefore PQ=\sqrt{(5-0{)}^2+(-3-1{)}^2}andQR=\sqrt{(0-x{)}^2+(1-6{)}^2}$

$\because$PQ = QR
$\Rightarrow \sqrt{(5-0{)}^2+(-3-1{)}^2}=\sqrt{(0-x{)}^2+(1-6{)}^2}$
$\Rightarrow \sqrt{(5{)}^2+(-4{)}^2}=\sqrt{(-x{)}^2+(-5{)}^2}$
$\Rightarrow \sqrt{25+16}=\sqrt{x^2+25}$
$\Rightarrow 41=x^2+25$
$\Rightarrow 16=x^2$
$\Rightarrow x=\pm 4$
Therefore, point R is (4, 6) or ( - 4, 6).