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In the rectangular coordinate system, what is the area of

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In the rectangular coordinate system, what is the area of [#permalink]

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Feb 2014, 07:19, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: Geometry in coordinate plane [#permalink]

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New post 19 Dec 2007, 12:38
mbsnyc wrote:
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


A

plot the points
make a square
subtract all the unnecessary triangles around the plotted triangle.

anyone know a faster way to do this?
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Re: Geometry in coordinate plane [#permalink]

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New post 19 Dec 2007, 12:41
bmwhype2 wrote:
mbsnyc wrote:
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


A

plot the points
make a square
subtract all the unnecessary triangles around the plotted triangle.

anyone know a faster way to do this?


use distance formula for each of the sides.

sides are 5 5 7
an isos rt triangle.
bh/2 = 5*5 / 2 = 12.5
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Re: Geometry in coordinate plane [#permalink]

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New post 19 Dec 2007, 12:45
How did you know it was a right triangle and not just isc?
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Re: Geometry in coordinate plane [#permalink]

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New post 19 Dec 2007, 12:45
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bmwhype2 wrote:
plot the points
subtract all the unnecessary triangles around the plotted triangle.


The same way
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Re: Geometry in coordinate plane [#permalink]

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New post 19 Dec 2007, 12:53
mbsnyc wrote:
How did you know it was a right triangle and not just isc?


you're right. its simply an isosceles triangle. we can infer the height is 7 but im not sure how to get the base.
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Re: Geometry in coordinate plane [#permalink]

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New post 19 Dec 2007, 14:00
mbsnyc wrote:
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


I get A.

Using the distance formula I get sides 5,5, 7

5*5/2=12.5
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Re: Geometry in coordinate plane [#permalink]

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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)|
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Re: In the rectangular coordinate system, what is the area of [#permalink]

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New post 14 Feb 2014, 11:03
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?
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Re: In the rectangular coordinate system, what is the area of [#permalink]

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New post 15 Feb 2014, 01:05
sanjoo wrote:
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?


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.
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Re: In the rectangular coordinate system, what is the area of [#permalink]

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New post 16 Feb 2014, 10:15
http://www.mathopenref.com/coordtrianglearea.html
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Re: In the rectangular coordinate system, what is the area of [#permalink]

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New post 09 Nov 2014, 22:50
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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
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Re: In the rectangular coordinate system, what is the area of [#permalink]

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New post 10 Nov 2014, 01:33
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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
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Re: In the rectangular coordinate system, what is the area of [#permalink]

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New post 29 Dec 2015, 13:48
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
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Re: In the rectangular coordinate system, what is the area of   [#permalink] 29 Dec 2015, 13:48
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