Question

The diagonals of rhombus MATH intersect at P(4,-5). If the equation of the line that

contains diagonal MT is y = -2x + 3, what is the equation of a line that contains
diagonal AH?
y = 1/2x +5
y = -1/2x-7
y = -2x + 5
y= 1/2x - 7

Answer 1

• D. y = 1/2x - 7

Explanation:

The diagonals of a rhombus are perpendicular:

• MT ⊥ AH

We have the equation for MT:

• y = -2x + 3

Perpendicular lines have negative-reciprocal diagonals, therefore AH has slope of 1/2.

Since AH passes through point (4, -5), the equation of the line is:

• y - (-5) = 1/2(x - 4)
• y = 1/2x - 2 - 5
• y = 1/2x - 7

Correct choice is D