[

Math Revolution GMAT math practice question]

Points A(1,4), B(2,2) and C(p,1) lie on the x-y coordinate plane. If lines AB and BC are perpendicular to each other, p=?

A. -2

B. -1

C. 0

D. 1

E. 2

=>

The slope of the line segment joining the two points (x

1,y

1) and (x

2,y

2) is (y

1-y

2)/(x

1-x

2). The product of the slopes of perpendicular lines is -1.

The slope of the line AB is (4-2)/(1-2) = -2.

Since the two lines AB and BC are perpendicular each other, the slope of BC, which is (2-1)/(2-p), must be 1/2.

So,

(2-1)/(2-p)=1/2

1/(2-p)=1/2.

Thus, 2 – p = 2, and p = 0.

Therefore, the answer is C.

Answer: C

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