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.
The slope of EF is.
The slope of GH is –2.
The slope of DF is –2.

Question:

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?

A. The slope of HI is 1/2.

B. The slope of EF is 1/2.

C. The slope of GH is –2.

C. The slope of DF is –2.

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

the answer to the expression is 83

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a