What is the slope of any line perpendicular to the line passing through (-17,23) and (21,25)?

2 Answers
Jul 11, 2018

"perpendicular slope "=-2

Explanation:

"calculate the slope m using the "color(blue)"gradient formula"

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

"let "(x_1,y_1)=(-17,23)" and "(x_2,y_2)=(21,25)

m=(25-23)/(21-(-17))=2/38=1/19

"the slope of any perpendicular line is"

•color(white)(x)m_(color(red)"perpendicular")=-1/m=-1/(1/19)=-19

-19

Explanation:

The slope m of straight line joining (x_1, y_1)\equiv(-17, 23) & (x_2, y_2)\equiv(21, 25)

m=\frac{y_2-y_1}{x_2-x_1}

=\frac{25-23}{21-(-17)}

=1/19

We know that the product of slope of two perpendicular lines is -1 then the slope of the straight line perpendicular to the given line joining #(-17, 23) & (21, 25)#

=-1/m

=-1/(1/19)

=-19