Question

The coordinates of P and Q are (-3, 4) and (2, 1), respectively. If PQ is extended to R such that PR = 2QR, then what are the coordinates of R ?

• A. (3, 7)
• B. (2, 4)
• C. $\left(-\frac{1}{2},\frac{5}{2}\right)$
• D. (7, - 2)

Answer 1

Answer: (D)

As given :
Coordinates of P and Q are (- 3, 4) and (2, 1) respectively.
Let coordinates of R be (x, y).
As given : PR = 2 QR
$\Rightarrow$ PR - QR = QR
$\Rightarrow$ PQ = QR.
So, Q is the mid point of P and R
$\Rightarrow 2=\frac{-3+x}{22}$ and $=\frac{4+y}{2}$
$\Rightarrow x=7$ and $y=-2$
$\therefore$ Coordinates of $R\equiv \left(7,-2\right)$