PQR is a right triangle in the xy plane

The solution to the Question shall be as follows:

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AREA shaded=?
State:1 sufficient
R=(3,8)
both triangle are simillar
RQ/PQ=Length of shaded triangle/base of shaded triangle
6/8=L/5
L=15/4 hence area shaded=1/2*5*15/4

state:2 not sufficient
no information about co ordinate of R
Answer A

PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?
1) The coordinate of point R is (3,8)
2) The coordinate of point Q is (3,2)

#1
The coordinate of point R is (3,8)
but we do not have the coordinate of point Q ; so insufficient

#2
The coordinate of point Q is (3,2)
but we do not have the coordinate of point R ; so insufficient
using 1 & 2
we have the points of ∆ PQR and shaded region area can be determined
OPTION C

PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?
Distance of base of shaded region is 5.

1) The coordinate of point R is (3,8) - No information about height of shaded region. So insufficient.

2) The coordinate of point Q is (3,2) - Base of shaded region is 2 point above from origin. Still insufficient.

1) + 2)

No exact information about height of shaded region. So insufficient.
Ans. E

Given: PQR is a right triangle in the xy plane.
Asked: If the coordinate of point P is (-5,2), what is the area of the shaded region?


1) The coordinate of point R is (3,8)
Since it is not provided that PQ is parallel to x-axis
Multiple right-triangles can be formed with P(-5,2) & R(3,8).
Area of shaded region = 1/2 * Base * height
Since k & m may vary and are unknown
NOT SUFFICIENT


2) The coordinate of point Q is (3,2)
Now PQ is parallel to x-axis
But since coordinate of R(3,y) is unknown
and correspondingly ordinate of A(0,k) is also unknown
NOT SUFFICIENT


(1) + (2)
1) The coordinate of point R is (3,8)
2) The coordinate of point Q is (3,2)
Now PQ is parallel to x-axis
Angle Q is right-angle
Since triangle PAB & PQR are similar triangles;
AB/PB = RQ/PQ
(x-2)/5 = (8-2)/(3+5) = 6/8 = 3/4
x = 2 + 15/4 = 5.75
Area of shaded region = 1/2 * 5 * (x-2) = 2.5(x-2) = 2.5*(5.75-2) = 2.5 * 3.75 = 9.375
SUFFICIENT

IMO C



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We know that point P is (-5,2) and PQR is a right triangle. Let the points where the y-axis cuts the triangle PQR be A (on side PR) and C (on side PQ) respectively. If P and Q have the same Y co-ordinate and R and Q have the same X co-ordinate, then triangles PQR and PCA will become similar triangles since all the 3 angles in the two triangles will be equal. If we know the co-ordinates of points R and Q, we can figure out the side lengths of triangle PQR. PC=5 since the x co-ordinate of P is -5. For similar triangles, we know that the ratios of the lengths of the corresponding sides are equal. And since we know one side of PCA, we can figure out the side AC and find the area of triangle PCA i.e the area of the shaded region.

(1) We have no information on the co-ordinates of point Q. Not sufficient.

(2) We have no information on the co-ordinates of point R. Not sufficient.

(1)+(2) Since we have the co-ordinates of points R and Q, we can find the area of the shaded region= Area of triangle PCA. Sufficient.

Answer: C.

Choice C is correct
PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?

Statement 1:
1) The coordinate of point R is (3,8)
We do not have enough information to find the area of the shaded area (triangle PAB)

Statement 2:
2) The coordinate of point Q is (3,2)
We do not have enough information to find the area of the shaded area

Both statements:
Since P and Q are located at y=2 and R and Q are located at X=3, we can find that PQ = 3-(-5) = 8 and RQ = 8-2 = 6

The area of triangle PRQ is 8*6/2 = 24

Triangles APB and RPB are similar because RQ is parallel to the Y-axis.
Since triangles APB and RPB are similar and we have the area of PRQ(=24), we can find the area of the shaded area PAB

This question is easier said than done.

Just use number sense and geometry common sense. We need all points P, Q R to find the area. Solving this question is very difficult. But in DS we do not need to solve the question hence the answer is C.

ANS: E BOTH INSUFFICIENT , SINCE WE CAN'T FIND HEIGHT OF THE SHADED REGION

Posted from my mobile device

Statement 1 is sufficient to answer the question.

slope is rise / run = (8-2)/(3+5) = 3/4. => for every 4 units forward, the line goes up by 3 unit. we know the distance of P from Y axis, we can find the height of the triangle and find the area.

One doubt might arise, what if the line PQ is not parallel to X-axis, since right angle triangle at q, we can drop perpendiculars from P and R and find the location of Q

PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?
1) The coordinate of point R is (3,8)
2) The coordinate of point Q is (3,2)

Statement 1 - R is (3,8) , which mean q will be (3,2)
we can get equation of line PR as we know two end point coordinates, using equation of line

we can also use similar triangle property to find length of base of SHADED area
hence sufficient

Statement - 2
does not give info on R and we cannot find coordinates of shaded triangle, hence not sufficient.

Answer- A
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PQR is a right triangle in the xy plane. If the coordinate of point P is (-5,2), what is the area of the shaded region?

(Statement1): The coordinate of point R is (3,8)
—> We cannot make sure whether the coordinate of point Q is (3,2) or not.
Insuffcient

(Statement2): The coordinate of point Q is (3,2).
—> the point of Q could be (3,8), (3.9) or any other points (3, y)
Insuffcient

Taken together 1&2,
PQ = 8
QR= 6
—> we can find the area of shaded region by using similar triangles:
5/8 = x/ 6
—> x= 30/8 = 15/4 = 3.75
Area of shaded region = 5*3.75/2 = 9.375
Sufffient

Answer (C)

Posted from my mobile device

i think " c" is the answer. two triangle are similar than the ratio of their sides are equal.

So we need both co-ordinates.

so "C" is the answer.

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