Question

A,B and C are the vertices of a triangle A has coordinates (4,6) B has coordinates (2,-2) C has coordinates (-2,-4) D is the midpoint of AB E is the midpoint of AC Prove that DE is parallel to BC

Answer 1

Answer:

Segments DE and BC have equal slopes, showing that segments DE and BC are parallel

Step-by-step explanation:

Here we have the coordinates as follows

The coordinates of A is (4, 6)

The coordinates of B is (2, -2)

The coordinates of C is (-2, -4)

Therefore, the coordinates of D the midpoint AB is ((4 + 2)/2, (6 - 2)/2) which gives;

The coordinates of D is (3, 2)

Similarly, the coordinates of E the midpoint AC is ((4 - 2)/2, (6 - 4)/2) which gives;

The coordinates of E is (1, 1)

To prove that segment DE is parallel to segment BC, e show that the slopes of the two segments are equal as follows;

$Slope \, of \, a \, segment = \frac{Change \, in \, the\ y \, coordinates}{Change \, in \, the\, x \, coordinates}$

$Slope \, of \, segment \ DE =\frac{2 - 1}{3-1} = \frac{1}{2}$

$Slope \, of \, segment \ BC =\frac{-2 - (-4)}{2-(-2)} = \frac{2}{4} =\frac{1}{2}$

Therefore, the slopes of segments DE and BC are equal, which shows that segment DE is parallel to BC.