Question

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Answer 1

The slope for is JK 1/3 , the slope of LK is -2 , the slope of ML is 2/5 , and the slope of MJ is 3/2 . Quadrilateral JKLM is not a parallelogram because neither pair of opposite sides is parallel

Further explanation:

Given vertices are:

J(−4, 1) , K(2, 3) , L(5, -3) , and M(0, −5) .

We have to find the slopes before concluding any result

The formula for slope is:

$m=\frac{y_2-y_1}{x_2-x_1}$

So:

Slope of JK:

$m_1=\frac{3-1}{2-(-4)}\\=\frac{2}{2+4}\\=\frac{2}{6}\\=\frac{1}{3}$

Slope of LK:

$m_2=\frac{-3-3}{5-2}\\=\frac{-6}{3}\\=-2$

Slope of ML:

$m_3=\frac{-3-(-5)}{5-0}\\=\frac{-3+5}{5}\\=\frac{2}{5}$

Slope of MJ:

$m_4=\frac{1-(-5)}{-4-0}\\=\frac{1+5}{-4}\\=\frac{6}{-4}\\=-\frac{3}{2}$

As the slopes of all sides are different, the given quadrilateral is not a parallelogram because in order for the quadrilateral to be a parallelogram the opposite sides have to be parallel i.e. have equal slopes and there are no sides with equal slopes.

Keywords: Parallelogram, Quadrilateral

Learn more about quadrilateral at;

• brainly.com/question/5191807
• brainly.com/question/5312408

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