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The y-intercepts, P and Q, of two perpendicular lines intersecting at

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Joined: 02 Sep 2009
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The y-intercepts, P and Q, of two perpendicular lines intersecting at  [#permalink]

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23 Apr 2019, 13:11
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Difficulty:

55% (hard)

Question Stats:

36% (02:47) correct 64% (03:21) wrong based on 11 sessions

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The y-intercepts, P and Q, of two perpendicular lines intersecting at the point A(6, 8) have a sum of zero. What is the area of triangle APQ ?

(A) 45
(B) 48
(C) 54
(D) 60
(E) 72

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Re: The y-intercepts, P and Q, of two perpendicular lines intersecting at  [#permalink]

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23 Apr 2019, 14:56
Let the pts of y intercept be P(0,y) and Q(0,-y).
Given A(6,8)

for perpendicular lines,
product of slopes=-1
(8-y)/6 *(8+y)/6=-1
8²-y²=-36
y²=100
y=10
So now P(0,10) Q(0,-10),A(6,8)

Now we have 2 options to calculate area of ∆PAQ either through 3 point determinant form or by calculating dist of perpendicular and base as ✓A is a right angle.

Let's calculate dist. of PA and PQ which is equal to √40 and √360.

so area of ∆PAQ= 0.5×√40×√360
=0.5×√40×3*√40= 40*3/2= 60.

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Re: The y-intercepts, P and Q, of two perpendicular lines intersecting at  [#permalink]

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27 Apr 2019, 02:05
Bunuel wrote:
The y-intercepts, P and Q, of two perpendicular lines intersecting at the point A(6, 8) have a sum of zero. What is the area of triangle APQ ?

(A) 45
(B) 48
(C) 54
(D) 60
(E) 72

plot value
we see y intercept both + ve and -ve are equal so (0,10) & (0,-10)
base = 20 ; altitude = 6 as point A (6,8)
so area ; 20 * 6/2 ; 60
IMO D
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Re: The y-intercepts, P and Q, of two perpendicular lines intersecting at   [#permalink] 27 Apr 2019, 02:05
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