Answer/Step-by-step explanation:
An easy way to be sure two lines are perpendicular is if the product of both slopes equals -1.
That is: [tex] (m_1)(m_2) = -1 [/tex]. Where, m1 and m2 are slopes of both lines respectively.
Let's find the slope of the both lines.
Slope of the line that slants upward from left to right using coordinates (0, 0) and (2, 2) of two points on the line:
[tex] m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} [/tex]
[tex] m_1 = 1 [/tex]
Slope of the line that slants downwards from left to right using coordinates (2, 2) and (0, 4) of two points on the line:
[tex] m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{0 - 2} = \frac{2}{-2} [/tex]
[tex] m_2 = -1 [/tex]
Find the product of both slopes
[tex] (m_1)(m_2) = (1)(-1) = -1 [/tex]
Therefore, we know the lines are perpendicular because [tex] (m_1)(m_2) = -1 [/tex].
