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kompoz [17]
4 years ago
11

Help with this please

Mathematics
1 answer:
Alik [6]4 years ago
7 0

Answer:

Yes, the given parallelogram is a rectangle.

Step-by-step explanation:

The vertices of parallelogram are J(-5,0), K(1,4), L(3,1) and M(-3,-3).

The slope formula is

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

JK=\frac{4-0}{1-(-5)}=\frac{4}{6}=\frac{2}{3}

KL=\frac{1-4}{3-1}=\frac{-3}{2}

LM=\frac{-3-1}{-3-3}=\frac{-4}{-6}=\frac{2}{3}

JM=\frac{-3-0}{-3-(-5)}=\frac{-3}{2}

The slopes of opposites sides are same it means they are parallel to each other.

The product of slopes of two consecutive sides is

\frac{2}{3}\times \frac{-3}{2}=-1

Since the product of slopes of two consecutive sides is -1, therefore the consecutive sides are perpendicular to each other.

Yes, the given parallelogram is a rectangle.

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