co-ordinate geometry

[francoisph]

Question # 23
The co-ordinates of the foot of the perpendicular from the point (2, 2) on the line y - 2x - 8 = 0 are

(A) (-1, 6)

(B) (-1, -4)

(C) (-2, 10)

(D) (2, 4)

(E) (-2, 4) answer

could you explain clearly?please

[albatross86]

Rewrite the line as y = 2x + 8

This is in slope intercept form and this tells us that the slope of our line is 2.

Now the perpendicular will therefore have a slope of -1/2

Start with E and use (y2 - y1) / (x2 - x1) = -1/2 so that the points (2,2) and the choices should validate this equation.

E. (-2,4) yields this very result and is hence our answer.

[ruplun]

Please can u explain , how the perpendicular slope is -1/2?

perpendicular will therefore have a slope of -1/2

[albatross86]

Please can u explain , how the perpendicular slope is -1/2?

perpendicular will therefore have a slope of -1/2

Sure.

It is a property of perpendicular lines that the product of their slopes will always be equal to -1.

This can be derived using Pythagorean theorem, but just remember it for the GMAT

Other important slopes:

1. 2 parallel lines will always have the same slope.
2. A line parallel to the x-axis has a slope of zero.
3. A line parallel to the y-axis has an undefined slope.

[outreach]

Slope of line y - 2x - 8 = 0 is 2
Slope of perpendicular(m) = -1/2 and it passed through (2,2). substitute this in eq of line to find the equation of perpendicular

Eq of line y=mx+c
2=-(1/2)2+c
therefore c=3
hence eq of perpendicular
y=-(1/2)x+3 -(1)
another line eq y - 2x - 8 = 0 is given in the eq
y - 2x - 8 = 0
y=2x+8 -(2)

solve eq 1 and 2 to find value of x and y
E