Triangle DEF is congruent to right triangle GHI with a right angle at vertex H. If the slope of DE is –2, what must be true?

The slope of HI is 1/2

The slope of EF is 1/2

Solution:

Given that,

Triangle DEF is congruent to right triangle GHI

Which means,

These pairs of angles are congruent

{D, G}, {E, H}, and {F, I}

In triangle DEF, E is a right angle

This means that the line segments are perpendicular.

We know that,

Product of slope of a line and slope of line perpendicular to that line is equal to -1

Given that,

Slope of DE = -2

Since the sides EF and HI are congruent,

Slopes of parallel lines are equal

Thus, Slope of HI is 1/2

b

step-by-step explanation:

given

- 2 (3x + 12y - 5 - 17x - 16y + 4 )

simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the parenthesis by - 2

= 28x + 8y + 2 → b