Question

Lines a and b are perpendicular. Which statements below must be true? Select all that apply. The slopes of lines a and b are reciprocals Line a and line b intersect at their midpoints. When the slopes of lines a and b are multiplied, the product is −1. Line a and line b intersect to form four right angles. The slopes of lines a and b are equal. The slopes of lines a and b are opposites

Answer 1

Answer:

When the slopes of lines a and b are multiplied, the product is −1.

Line a and line b intersect to form four right angles.

Step-by-step explanation:

Given

Perpendicular lines a and b

Required

Select the true statements

Represent the slope of line a with $m_1$ and the slope of b with $m_2$.

The condition for perpendicularity is:

$m_1 * m_2 = -1$

Solving further:

$m_1 = -\frac{1}{m_2}$

To solve further, we need to analyze each of the given options

(a) This is not true because the slope of perpendicular lines are not reciprocal

(b) This is also not true because perpendicular lines do not necessarily have to intersect at their midpoints

(c) This is true because of the condition stated above: $m_1 * m_2 = -1$

(d) This is also true because perpendicular lines form right angles when they intersect

(e) This is not true because of the condition stated above: $m_1 = -\frac{1}{m_2}$

(f) This is not true because of the condition stated above: $m_1 = -\frac{1}{m_2}$