What are the coordinates of the foot of the perpendicular from the

The given line is y=2x+8 so the slope of the perpendicular is -1/2
Let us say the equation is y=-(1/2)x+c
Since this line passes through (2,2), let us substitute the values to get c
2=-(1/2)*2+c
So c=3
So the equation of the perpendicular is y=-(1/2)x+3
Since the question asks for the foot of the perpendicular on the given line, it means we need the point that lies on both the line and the perpendicular. At that point the y coordinate has to be the same for both the lines. So let us equate
We get 2x+8=-(1/2)x+3
Solving, (5/2)x=-x=-2
E is the only choice that has -2 as the x coordinate
Hence E

Posted from my mobile device

Foot of perpendicular from point (2,2) must also lie on the given line y-2x-8 =0.

Therefore, When it is put in the above equation must satisfy it.

Given line y = 2x + 8
Putting the given coordinates in the above Line equation, we get

A. -2 = 2x4 + 8 ⇒ -2 = 16 (Does not satisfy) ⇒ Reject
B. 2 = 2x-4 +8 ⇒ 2 = 0 (Does not satisfy)⇒ Reject
C. 4 = 2x2 + 8 ⇒ 4 = 12 (Does not satisfy)⇒ Reject
D.-4 = 2x2 + 8 ⇒ -4 = 12 (Does not satisfy)⇒ Reject
E. 4 = 2x-2 + 8 ⇒ 4 = 4 (Satisfies)- Accepted - Correct answer.

Rule 1: the "Foot" of the Perpendicular from Point (2 , 2) to the Line given by y - 2x - 8 = 0 will be the Point at which the Line connected to (2 , 2) will be PERPENDICULAR to the Line given by y - 2x - 8 = 0

Rule 2: the Slop of a Perpendicular Line is the (-)Neg. Reciprocal of the Original Line's Slope


y - 2x - 8 = 0

In Slope Intercept Form:

y = 2x + 8

Slope = m = +2

The (-)Negative Reciprocal of +2 ----- (-)1/2


Thus, the Perpendicular Line must be of the Form: y = (-)1/2x + b

We know that this Line must Intersect Point (2, 2). So we can Plug this Point into the Equation to find the Y-Intercept = b

y = (-)1/2x + b

2 = (-)1/2 * (2) + b

2 = -1 + b

b = 3

The Equation of the Line: y = -1/2x + 3


Finally, we can find the exact Point by setting the 2 Equations Equal and Find the X-Coordinate of their Intersection

y = 2x + 8 = -1/2x + 3 = y

4x + 16 = -1x + 6

5x = -10

x = -2

The Y-Coordinate is given as, after plugging in x = -2:

y = -1/2 * (-2) + 3

y = 4


The Answer is: (X , Y) = (-2 , 4)

-E-

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.