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Coordinate Geometry

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avatar+154 
Hi,

there are a few coordinate geometry problems giving me trouble:

1. "The vertices of a right triangle are S(-2,-2), (T(10, -2), and R(4,5). Find the area of the triangle."

(I got 42 square units as the answer but the book says the answer is actually 36 square units...)

2. What type of triangle do the vertices A(4, 2), B(-2, -2) and C(2, -8) belong to? Determine the answer without plotting the points on a graph.
a) scalene
b) isosceles
c) equilateral

3. The coordinates of the endpoints of the diameter of a circle are (6,4) and (-2,0). Find the length of the radius of the circle.

Thanks!
 Mar 11, 2014

2+0 Answers

 #1
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Your answer of 42 is correct. Let ST be the base and R be the apex point. Then, the length of the base is 12. This triangle is isosceles with RS = RT. A perpendicular drawn from the midpoint of the base, (4,-2), will go through R, so this is the height which, by the distance formula, is just = 7. Therefore, the area = (1/2)*B*H - (1/2)*(12)*(7) = 42.

2. The triangle is isosceles..

First, find the distances between AB, BC and AC using the distance formula.
AB = SQRT(52)
BC = SQRT(52)
AC = SQRT (104)

Since AB = BC, the triangle is isosceles.

3. This one should be pretty easy. Just use the distance formula to find the distance between the endpoints. This = SQRT(80) = 4*SQRT(5). Take half of this to get the radius = 2*SQRT(5)

Hope this helps.....
 Mar 12, 2014
 #2
avatar+154 
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Thank you, that did indeed help.
 Mar 13, 2014

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