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Hoochie [10]
3 years ago
14

Points A(-2,4) , B(1,3), C(4,1) and D form a parallelogram.What are the coordinates of D?

Mathematics
1 answer:
frez [133]3 years ago
6 0

Answer:

The coordinates of vertex D are (1,2).

Step-by-step explanation:

Let the coordinates of D are (a,b).

It is given that ABCD is a parallelogram and the vertices of the parallelogram are A(-2,4), B(1,3) and C(4,1).

According to the property of parallelogram, the diagonals of the parallelogram bisect each other.

AC and BD are diagonals of the parallelogram ABCD.

Midpoint formula:

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Using midpoint formula, the midpoint of AC is

Midpoint_{AC}=(\frac{-2+4}{2},\frac{4+1}{2})=(1,\frac{5}{2})

Using midpoint formula, the midpoint of BD is

Midpoint_{BD}=(\frac{1+a}{2},\frac{3+b}{2})

Midpoint of both diagonals is the intersection point of the diagonals.

Midpoint_{AC}=Midpoint_{BD}

(1,\frac{5}{2})=(\frac{1+a}{2},\frac{3+b}{2})

On comparing both the sides we get

1=\frac{1+a}{2}

2=1+a

2-1=a

1=a

The value of a is 1.

\frac{5}{2}=\frac{3+b}{2}

5=3+b

5-3=b

2=b

The value of b is 2.

Therefore the coordinates of vertex D are (1,2).

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