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

The coordinates of D is (3, 2)

The coordinates of E is (1, 1)

gradient of BC is -2/-4, which is 1/2

gradient of DE is-1/-2, which is 1/2

The gradients are the same, making it parallel

Explanation:

Full mark answer on maths watch, copy and paste

Answer 2

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

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 = (Change \, in \, the\ y \, coordinates)/(Change \, in \, the\, x \, coordinates)`

`Slope \, of \, segment \ DE =(2 - 1)/(3-1) = (1)/(2)`

`Slope \, of \, segment \ BC =(-2 - (-4))/(2-(-2)) = (2)/(4) =(1)/(2)`

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