Question

A walking path across a park is represented by the equation y = -2x+ 5. A

new path will be built perpendicular to this path. The paths will intersect at
the point (-2,9). Identify the equation that represents the new path.
Help

Answer 1

`y = (1)/(2)x+10`

Explanation:

The given path is:

y = -2x+5

Comparing with the standard form of equation:

y = mx+b

So,

m = -2

We know that product of slopes of two perpendicular lines is -1

Let m1 be the slope of the perpendicular line

m*m1=-1

-2*m1 = -1

m1 = -1/-2

m1 = 1/2

So the slope of perpendicular path is 1/2.

Since the new path passes through (-2,9)

`9 = (1)/(2)(-2) +b\\9 = -1 +b\\b = 10`

Putting the values of m and b in standard form

`y = (1)/(2)x+10`

Hence the equation of new path is:

`y = (1)/(2)x+10` ..