In the rectangular coordinate system above, the area of triangular reg

Question

https://gmatclub.com/forum/download/file.php?id=42073 In the rectangular coordinate system above, the area of triangular region PQR is A. \frac{ac}{2} B. \frac{(c-a)(b-d)}{2} C. \frac{(c+a)(b+d)}{2} D. \frac{c(b-d)}{2} E. \frac{c(b+d)}{2} xy (1).jpg

Nikhil · Accepted Answer

Area = \frac{1}{2} * base * height

Let the point where PR intersect x-axis is S. The co-ordinates of S will be (a,0)

the base of the triangle is PR
the height of the triangle is QS

Co-ordinates of P and Q are (a,b) and (a,d) respectively

base = |b| + |d| = b-d (since |b| = b as it is y co-ordinate in 2nd quadrant and |d|=-d as it is the y co-ordinate in 3rd quadrant)
height = |c| - |a| = c-a (since |c| = c as it is x co-ordinate in 1st quadrant and |a|=-a as it x co-ordinate is in 2nd quadrant)

Hence  Area = \frac{(c-a)(b-d)}{2}

Hence  option B

GyMrAT · Answer

Base = c + a

Height = b + d

Area =   \frac{(c+a)(b+d)}{2}

Answer C.

Thanks,
GyM

Nikhil · Answer

The value of a will be -1, -2 ,-3 etc since it is x-coordinate and it is in left half of x-axis. So we need to add |a| to c. If we simply add 'a' to value of c, we don't get the correct height. Same is the case for b+d

MHIKER · Answer

Area=\frac{1}{2}*base*height

Base=b-d, \ Height=c-a

\frac{1}{2}*  \frac{(c-a)(b-d)}{2}

The answer is  B.

warrior1991 · Answer

We have base as PR and height as QS where S is the intersection point of P and R at the X axis.

Point =(a,0)
Base=PR=|b|+|d|
Here the b is in second quadrant where it takes the +ve value. Therefore |b| =b
d is in the 3rd quadrant where it takes -ve value. Therefore |d|=-d

Height=|a|+|c|
|a|=-a because it is on left side of the vertical y axis
|c|=c because it is on right side of the vertical y axis.

Area=1/2*b*h
So area =1/2* (b-d)(c-a)

B is correct.

In the rectangular coordinate system above, the area of triangular reg

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In the rectangular coordinate system above, the area of triangular reg

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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