Question

In the figure above, line $\iota$ (not shown) is perpendicular to segment $AB$ and bisects segment $AB$. Which of the following points lies on line $\iota$?

• A. $(0,2)$
• B. $(1,3)$
• C. $(3,1)$
• D. $(3,3)$
• E. $(3,6)$

Answer 1

The correct option is D $(3,3)$

Given line l bisects AB and perpendicular to AB.

To find point lie on the line

Slope of the line perpendicular to AB

$m_1{m}_2=-1-1m_2=-1m_2=1$

And it will pass through the midpoint of AB

Let coordinates of midpoint be $(x,y)$

$x=\frac{0+2}{2}=1y=\frac{0+2}{2}=1(x,y)=(1,1)$

So equation of line passing through $(1,1)$ and having slope $m=1$

$(y-1)=1\times (x-1)y-1=x-1y=x$

Hence $(3,3)$ be the point that lie on this line.