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

Explanation:

slope of first road
`m_(1) =(7+8)/(2+5) =(15)/(7) \\slope~of~second~road~m_(2)=(y-1)/(10+5) =(y-1)/(15) \\as~roads~are~perpendicular.\\</p><p>m_(1)*m_(2)=(15)/(7) *(y-1)/(15) =-1\\</p><p>or~y-1=-7\\y=-7+1=-6`

Answer 2

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

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=(7-(-8))/(2-(-5))=(7+8)/(2+5)=(15)/(7)`

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

`m_2=(y-1)/(10-(-5))=(y-1)/(10+5)=(y-1)/(15)`

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

`m_1* m_2=-1\\\\\Rightarrow\ (15)/(7)*(y-1)/(15)=-1\\\\\Rightarrow\ y-1=-7\\\\\Rightarrow\ \ y=-7+1=-6`

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