Question

Is the line that contains the points (3,5) and

Answer 1

m₁ ≠ -1/m₂

So, the lines, line 1 and line 2 are not perpendicular.

Step-by-step explanation:

For finding if the two lines are perpendicular, we will find the slope of two lines and if slope of line 1= -1/slope of line 2 then the lines are perpendicular

Finding slope of line 1 (m₁)

line 1 that contains the points (3,5) and  (-3,3)

$slope = \frac{y_{2}-y_{1}}{x{2}-x_{1}} \\Where\,\, y_{2}=3,y_{1}=5,x{2}=-3,x_{1}=3\\slope =\frac{3-5}{-3-3}\\slope=\frac{-2}{-6}\\slope=\frac{1}{3}$

So, $m_{1}=\frac{1}{3}$

Finding slope of line 2 (m₂)

$slope = \frac{y_{2}-y_{1}}{x{2}-x_{1}} \\Where\,\, y_{2}=4,y_{1}=5,x_{2}=-4,x_{1}=2\\slope =\frac{4-5}{-4-2}\\slope=\frac{1}{-6}\\slope=-\frac{1}{6}$

So, $m_{2}=\frac{1}{6}$

Since, m₁ ≠ -1/m₂

So, the lines, line 1 and line 2 are not perpendicular.

Keywords: Perpendicular lines

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