Question

Two cars are traveling on two different roads that are perpendicular to each other. On a coordinate map, the first car started from the point (-5,-8) and stopped at (2,7). The second car started at (-5,1) and stopped at (10,y).
The y-coordinate of the second car is ______?

Answer 1

Answer:

Step-by-step explanation:

slope of first road$m_{1} =\frac{7+8}{2+5} =\frac{15}{7} \\slope~of~second~road~m_{2}=\frac{y-1}{10+5} =\frac{y-1}{15} \\as~roads~are~perpendicular.\\m_{1}*m_{2}=\frac{15}{7} *\frac{y-1}{15} =-1\\or~y-1=-7\\y=-7+1=-6$

Answer 2

Answer: The y-coordinate of the second car is -6.

Step-by-step explanation:

Given : Two cars are traveling on two different roads that are perpendicular to each other.

Slope of first car started from the point (-5,-8) and stopped at (2,7):

$m_1=\dfrac{7-(-8)}{2-(-5)}=\dfrac{7+8}{2+5}=\dfrac{15}{7}$

Slope of second car started at (-5,1) and stopped at (10,y) :

$m_2=\dfrac{y-1}{10-(-5)}=\dfrac{y-1}{10+5}=\dfrac{y-1}{15}$

Since both cars perpendicular, then the product of their slope is equals to -1.

$m_1\times m_2=-1\\\\\Rightarrow\ \dfrac{15}{7}\times\dfrac{y-1}{15}=-1\\\\\Rightarrow\ y-1=-7\\\\\Rightarrow\ \ y=-7+1=-6$

Hence, The y-coordinate of the second car is -6.