Question #dccca

The slope of a line can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

The slope of the line passing through `(-3, 4)` and `(1, 2)` is:

`m_1 = (color(red)(2) - color(blue)(4))/(color(red)(1) - color(blue)(-3)) = (color(red)(2) - color(blue)(4))/(color(red)(1) + color(blue)(3)) = -2/4 = -1/2`

The slope of the line passing through `(-1, 3)` and `(1, 1)` is:

`m_2 = (color(red)(1) - color(blue)(3))/(color(red)(1) - color(blue)(-1)) = (color(red)(1) - color(blue)(3))/(color(red)(1) + color(blue)(1)) = -2/2 = -1`

Given a line with slope `m`, a line perpendicular to this line, let's call it `m_p` will have a slope the negative inverse of the original line. Or:

`m_p = -1/m`

The line perpendicular to the first line therefore would have a slope:

`m_(p1) = (-1)/(-1/2) = 2`

This is not the slope of the second line therefore these two lines are not perpendicular.

Slope `m=(y2-y1)/(x2-x1)`
And for 2 lines to be perpendicular the product of their slopes must be = -1
Therefore on finding the slopes we get
`m1=(2-4)/(1-(-3)) = -1/2`
`m2=(1-3)/(1-(-1)) = -2/2 = -1`
But `m1*m2 != -1`
Hence they are not perpendicular
Hope u find it helpful :)