Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4) and the coordinates of M are M(3,-2) find the slopes of sides KL,LM,MN,and NK

We can start by finding the gradient of LM
[tex]m= \frac{ y_{2}- y_{1} }{x_{2} - x_{1} } = \frac{-2--4}{3-1} = \frac{2}{2}=1 [/tex]

Two perpendicular lines will meet the requirement [tex]m_{1} [/tex]×[tex]m_{2} [/tex]=-1
Two parallel lines have equal gradients

NM is perpendicular to LM, hence the gradient of NM is -1
KN is a line that is parallel to NM, hence the gradient is 1
KL is perpendicular to LM, hence the gradient of KL is -1

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DelcieRiveria DelcieRiveria · Answer 2 · 2019-05-28T13:02:06+02:00

Answer:

The slope of LM is 1, slope of KL is -1, slope of MN is -1 and the slope of NK is 1.

Step-by-step explanation:

It is given that quadrilateral KLMN is a rectangle and the coordinates of L are L(1,-4) and the coordinates of M are M(3,-2).

If a line passing though two points, then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The slope of LM is

[tex]m_{LM}=\frac{-2-(-4)}{3-1}=1[/tex]

The slope of LM is 1.

Two consecutive sides of a rectangle are perpendicular and the product of slopes of two perpendicular lines are -1.

[tex]m_{KL}\times m_{LM}=-1[/tex]

[tex]m_{KL}\times 1=-1[/tex]

[tex]m_{KL}=-1[/tex]

The slope of KL is -1.

The opposite sides of a rectangle are parallel and the slope of parallel lines are same.

Therefore, the slope of MN is -1 and the slope of NK is 1.