Question

Is the line through points P(2,-9) and Q(6, -13) perpendicular to the line through points R(5,-1) and

S(1,-5)?

Answer 1

Two lines
`y_1,y_2` are perpendicular if their slopes are in a relation
`m_1=-(1)/(m_2)`.

So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.

To find slopes, use slope formula

`m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1)`

The first slope of a line passing through
`PQ` is

`m_1=(-13-(-9))/(6-2)=(-4)/(4)=-1`

The second slope of a line passing through
`RS` is

`m_2=(-1-(-5))/(5-1)=(4)/(4)=1`

Now check if
`m_1=-(1)/(m_2)` is true

`-1=-(1)/(1)\implies -1=-1`

This means the two lines are perpendicular.

Hope this helps.