Question

two cars are traveling on two different roads that are perpendicular to each other. on a coordinate map, the first started from the point (-3,2) and stopped at (1,-2). the second car started from (-1,-2) and stopped at (3,y). what is the y-coordinate of the final destination of the second car?

Answer 1

Since the roads are perpendicular to each other. And for perpendicular lines, product of slopes is equal to -1 .

So for the first car , with the points ,  (-3,2),(1,-2), slope is

$m_{1} = \frac{-2-2}{1-(-3)} = \frac{-4}{4} = -1$

And for the second car, with points (-1,-2),(3,y), slope is

$m_{2} = \frac{y-(-2)}{3-(-1)} = \frac{y+2}{4}$

And product of slopes have to be -1, that is

$m_{1}*m_{2} =-1$

Substituting the values of the two slopes

$=> -1* \frac{y+2}{4} =-1 \\ =>\frac{y+2}{4} =1$

Multiplying both sides by 4

$y+2 =4 \\ y=4-2 \\ y=2$

And that's the missing value of y coordinate .