In the rectangular coordinate system, what is the area of

Question

In the rectangular coordinate system, what is the area of triangle PQR with points

Q=(0,3)
R=(7,4)
P(4,0)

A. 12.5
B. 14
C. 10
D. 16
E. 25

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Official Answer

A

Sunny143 · Accepted Answer

The area of a triangle with co-ordinates (x1,y1), (x2,y2), (x3,y3) is

1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

bmwhype2 · Answer

A

plot the points
make a square
subtract all the unnecessary triangles around the plotted triangle.

anyone know a faster way to do this?

bmwhype2 · Answer

use distance formula for each of the sides.

sides are 5 5 7
an isos rt triangle.
bh/2 = 5*5 / 2 = 12.5

mbsnyc · Answer

How did you know it was a right triangle and not just isc?

walker · Answer

The same way

bmwhype2 · Answer

you're right. its simply an isosceles triangle. we can infer the height is 7 but im not sure how to get the base.

GMATBLACKBELT · Answer

I get A. 

Using the distance formula I get sides 5,5, 7

5*5/2=12.5

sanjoo · Answer

can we do this by distance formula..

square root (x2-x1)^2+(y2-y1)^2

I did that by this formula.. M geting 5, 5 and square root 50 respectively of three sides... so 5*5/2=12.5 Ans A.

is it rite? whats another aproach?

Manofsteel · Answer

Yes you can do it with this formula... simplest and fastest approach.
 There are other approaches mentioned in the posts but those involve more steps. Like plotting a trapezium finding its area and then subtracting two 3-4-5 rt angled triangles to get the desired area.

ConnectTheDots · Answer

https://www.mathopenref.com/coordtrianglearea.html

quijotes · Answer

To figure out if it's a right triangle we should figure out if two of the sides are vertical to each other.

side 1 coordinates are 0,3 and 4,0 => slope = -3/4
side 2 coordinates are 4,0 and 7,4 => slope = 4/3

slope side1 / slope side2 = (-3/4)/(4/3) = -1
sides are perpendicular to each other and the triangle is right.

Now you can calculate
side1 = 5
side2 = 5
area = (side1 x side2) / 2 = 12.5

Temurkhon · Answer

we should count all three sides of PQR, so we get

5,5,5*sqrt2, meaning it is right triangle with 45, 45, 90 degree angles

so we only need to 5*5/2=12.5

A

hdwnkr · Answer

Adding to the diagram by  walker , if once calculates the area of the triangle that has QR as the hypotenuse, it comes to be a non-integer, which subtracted from a whole integer (28) would give a non integer.

The only non integer options is A

Bunuel · Answer

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In the rectangular coordinate system, what is the area of

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GMAT Problem Solving (PS) Questions

In the rectangular coordinate system, what is the area of

Prep Toolkit

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