Question

On a coordinate plane, 2 lines are shown. Line M N goes through (negative 4, 8) and (negative 4, negative 6). Line K L goes through (negative 8, 2) and (6, 2). How are lines KL and MN related? The lines intersect at point K. The lines are parallel. The lines are perpendicular. The lines do not have slopes.

Answer 1

Option 3.

Explanation:

It is given that the line MN passes through the point (-4,8) and (-4,-6). The line KL passes through the points (-8,2) and (6,2).

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the slope of the line is

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

The slope of the line MN is

`m_(MN)=(-6-8)/(-4+4)=\infty`

It means line MN is a vertical line.

The slope of the line KL is

`m_(KL)=(2-2)/(6-(-8))=0`

It means line KL is a horizontal line.

Vertical and horizontal line are perpendicular. So, lines KL and MN are perpendicular.

Therefore, the correct option is 3.

Answer 2

The lines are perpendicular.

Explanation:

We are given that on a coordinate plane

Line MN passing through (-4,8) and (-4,-6).

Line KL passing through (-8,2) and (6,2).

We have to find the relation between KL and MN.

Slope of line when line passing through the point
`(x_1,y_1)` and
`(x_2,y_2)` is given by

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

Using the formula

Slope of line MN=
`(-6-8)/(-4+4)=-\infty`

Slop of line KL=
`(2-2)/(6+8)=0`

Slope of line MN=
`-(1)/(slope\;of\;line\;KL)`

When slope of lines are reciprocal to each other then the lines are perpendicular.

Hence, line KL and MN are perpendicular.

Answer:The lines are perpendicular.