Question

The endpoints of DE and D(-3, y) and x, 6). The midpoint of DE is M(4,2). What is the length of DE.

Answer 1

If the endpoints of DE where D(-3, y) and E(x, 6) with the midpoint M(4, 2), the length of DE is 16.12 units

The formula for calculating the midpoint is expressed as;

$M(x,y)=(\frac{x_1+x_1}{2}, \frac{y_1+y_2}{2})$

For the x-coordinate points:

X = -3+x/2

4 * 2 = -3 + x

8 = -3 + x

x = 8 + 3

x = 11

Get the value of y;

2 = y+6/2

y+6 = 2 * 2

y + 6 = 4

y = 4 - 6

y = -2

Hence the coordinates of D and E are D(-3, -2) and E(11, 6)

$D=\sqrt{(6-(-2))^2+(11-(-3))^2}\\D=\sqrt{8^2+14^2}\\D=\sqrt{64 + 196}\\D= \sqrt{260}\\D= 16.12units$

Hence the length of DE is 16.12 units

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