Question

In exercises 27-30, three vertices of DEFG are given. Find the coordinates of the remaining vertices: D(-2,-4), F(0,7), G(1,0)

Answer 1

Answer:

$E =$ $(-3,3)$

Step-by-step explanation:

Given

Parallelogram: DEFG

$D(x_1,y_1) = (-2,-4)$

$F(x_3,y_3) = (0,7)$

$G(x_3,y_4) = (1,0)$

Required

Find the coordinates of $E(x_2,y_2)$

To do this, we make use of mid-point formula which is:

$M = (\frac{x_1+x_3}{2},\frac{y_1+y_3}{2})= (\frac{x_2+x_4}{2},\frac{y_2+y_4}{2})$

This gives:

$(\frac{-2+0}{2},\frac{-4+7}{2})= (\frac{x_2+1}{2},\frac{y_2+0}{2})$

$(\frac{-2}{2},\frac{3}{2})= (\frac{x_2+1}{2},\frac{y_2+0}{2})$

Multiply through by 2

$2 * (\frac{-2}{2},\frac{3}{2})= (\frac{x_2+1}{2},\frac{y_2+0}{2})*2$

$(-2,3) = (x_2+1,y_2+0)$

$(-2,3) = (x_2+1,y_2)$

By comparison:

$-2 = x_2 + 1$ and $3= y_2$

So, we have:

$-2-1=x_2$ and $3= y_2$

$-3 = x_2$ and $3 = y_2$

This gives:

$x_2 = -3$ and $y_2 =3$

Hence, the 4th coordinate is: $(-3,3)$