The product of the slopes of perpendicular lines equals what?

The product of the slopes of perpendicular lines equals -1

Solution:

Need to determine product of slope of perpendicular lines.

Product of slopes of perpendicular lines is always equal to -1.

lets verify this.

let consider following two equation of perpendicular lines

2x – y = 1

x + 2y = 2

Now evaluate slope of each line by representing them in slop intercept form that is y = mx + c

Where coefficient of x represents slope m.

Representing first line in slope intercept form we get

y = 2x – 1

On comparing above equation with slope intercept form we can say that its slope is 2.

Similarly representing x + 2y = 2 equation in slope intercept form we get

On comparing above equation with slope intercept form we can say that its slope is

On multiplying slopes of two perpendicular lines we get,

Hence product of slope of perpendicular line is -1

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl