Question

I have this thing I have to do for homework but in unsure of how to do it.

Answer 1

To check if those segments are parallel, we can compare the slope of the lines that contain them. To find the slope using two points, we can use the following formula

`m=((y_2-y_1))/((x_2-x_1))`

Using this formula for the segment AB, we have

`m_1=\frac{((-2)-3)}{((-12)-(-8))_{}}=(-5)/(-12+8)=(5)/(4)`

Now, using this formula for CD

`m_2_{}=\frac{((-7)-(-3))}{((-2)-(-7))_{}}=(-7+3)/(-2+7)=-(4)/(5)`

When the slopes are equal, the lines are parallel, if one slope is minus the inverse of the other, they are perpendicular, otherwise they are neither.

Since

`(5)/(4)=-(-(4)/(5))^(-1)\Rightarrow m_1=-(1)/(m_2)`

They are perpendicular.