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 [tex]m_1[/tex] and the slope of b with [tex]m_2[/tex].
The condition for perpendicularity is:
[tex]m_1 * m_2 = -1[/tex]
Solving further:
[tex]m_1 = -\frac{1}{m_2}[/tex]
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: [tex]m_1 * m_2 = -1[/tex]
(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: [tex]m_1 = -\frac{1}{m_2}[/tex]
(f) This is not true because of the condition stated above: [tex]m_1 = -\frac{1}{m_2}[/tex]
The product of the slope of the perpendicular lines is negative of one. Then the correct options are B and C.
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Lines a and b are perpendicular.
Then the product of the slope of the perpendicular lines is negative of one. That is given as
[tex]\rm m_1*m_2 = -1[/tex]
a. The slopes of lines a and b are reciprocals Line a and line b intersect at their midpoints. This is false.
b. When the slopes of lines a and b are multiplied, the product is −1. This is true.
c. Line a and line b intersect to form four right angles. This is true.
d. The slopes of lines a and b are equal. This is false.
e. The slopes of lines a and b are opposites. This is false.
More about the linear system link is given below.
https://brainly.com/question/20379472
