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 $PQ$, the M must lie on the line represented by

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

Answer 1

The correct option is B $y=5x-7$

$P$ is a point on the graph of $y=5x+3$

So, coordinates of point $P$ will be $(x,5x+3)$

Coordinates of Point $Q$ are $(3,-2)$

Let Coordinates of Point $M$ are $(h,k)$, which is the mid-point of $PQ$

then,

$h=\frac{x+3}{2}$ and $k=\frac{-2+5x+3}{2}$

Now,

$h=\frac{x+3}{2}$

$x+3=2h$

$x=2h-3$ ............ (1)

$k=\frac{-2+5x+3}{2}$

$k=\frac{5x+1}{2}$

$5x+1=2k$

$5x=2k-1$

$x=\frac{2k-1}{5}$ .............. (2)

From (1) and (2),

$2h-3=\frac{2k-1}{5}$

$2k-1=10h-15$

$2k=10h-14$

$k=5h-7$

Replace $h$ with $x$ and $k$ with $y$ to find the locus of point $M$

$y=5x-7$