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ELEN [110]
3 years ago
5

Three vertices of parallelogram JKLM are J(1, 4), K(5, 3), and L(6,−3). Find the coordinates of vertex M.

Mathematics
1 answer:
Andrej [43]3 years ago
5 0

Answer:

coordinates of vertex M is (x, y) = (2, -2)

Step-by-step explanation:

Since JKLM is a  parallelogram, this implies that JK parallel to LM and KL parallel to JM. This means that

Slope of JK = slope of LM

\frac{3-4}{5-1} =\frac{-3-y}{6-x} \\y=-\frac{1}{4}x-\frac{3}{2} ....(i)

And

Slope of KL = slope of JM

\frac{3-\left(-3\right)}{5-6}=\frac{4-y}{1-x}\\y=10-6x...(ii)

From equation (i) and (ii) we get

-\frac{1}{4}x-\frac{3}{2} =10-6x

-\frac{23x}{4}=-\frac{23}{2}

-23x=-46

x=2

Put the value of x in equation (ii) we get

y=10-6(2)\\y=-2

So, the coordinates of vertex M is (x, y) = (2, -2).

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