Question

P is a point on the graph of $y=5x+3$. The coordinates of a point Q are $(3,-2)$. If $M$ is the mid-point of $PQ,$ then $M$ must lie on the line represented by

• A. $y=5x+1$
• B. $y=5x-7$
• C. $y=\frac{5}{2}x-\frac{7}{2}$
• D. $y=\frac{5}{2}x+\frac{1}{2}$

Answer 1

Answer: (B)

$y=5x-7$

Let P be any point of $y=5x+3$

Then, P $=(h,5h+3)$ and Q $=(3,-2)$

$\therefore$ M $=(\frac{h+3}{2},\frac{5h+1}{2})$

M must lie on the line $y=5x-7$.(as M satisfies this equation)