Question

If (2, 3, -1) is the midpoint of AB where A=(-1,5,3) then B =

• A. (5, 1, -5)
• B. (5, -1, 5)
• C. (-5, 1, 5)
• D. NONE OF THESE

Answer 1

The correct option is A (5, 1, -5)

Given, $(2,3,-1)$ is mid point

then it will divide $AB$ in $1:1$

let, $B$ be $(x,y,z)$

so, according to section formula

$(\frac{1x+1(-1)}{1+1},\frac{1y+1\left(5\right)}{1+1},\frac{1z+1\left(3\right)}{1+1})=(2,3,-1)$

$(\frac{x-1}{2},\frac{y+5}{2},\frac{z+3}{2})=(2,3,-1)$

$⟹\frac{x-1}{2}=2$

$⟹x-1=4$

$⟹x=5$

Also,$\frac{y+5}{2}=3$

$⟹y+5=6$

$⟹y=6-5=1$

Also,$\frac{z+3}{2}=-1$

$⟹z+3=-2$

$⟹z=-2-3=-5$

hence,$B=(5,1,-5)$