SOLUTION: Determine the area of the right triangle with vertices R(4,4), S(-2,-2), and T(10,-2).

Algebra.Com
Question 1159866: Determine the area of the right triangle with vertices R(4,4), S(-2,-2), and T(10,-2).
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The y-coordinates of S and T are the same, so side ST is horizontal, with length 10-(-2) = 12.

So we can use ST as the base; the height of the triangle is then just the distance from the line y=-2 to the point (4,4), which is 4-(-2) = 4+2=6.

Then the area is one-half base times height:

Alternatively (but I think it is more work), you could use the fact that it is a right triangle, with legs RS and RT, so the area is one-half the product of the lengths of those legs.

The length of each leg is ; then the area is

But that, like I said, was more work....
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Determine the area of the right triangle with vertices R(4,4), S(-2,-2), and T(10,-2).
===========
Another method:
   R   S   T   R
x  4  -2  10   4
y  4  -2  -2   4

----------------
Add the diagonal products starting at the upper left:
--> 4*(-2) + -2*-2 + 10*4 = -8 + 4 + 40 = 36
----
Add the diagonal products starting at the lower left:
--> 4*-2 + -2*10 + -2*4 = -8 -20 - 8 = -36
The difference is 72.
The area is 1/2 that, = 36 sq units.
=======================
Might be the "hard way" for a triangle, but it works for any plane figure, with any # of sides.
The points must be entered in order around the figure is the only restriction.

RELATED QUESTIONS

Determine whether the three points are the vertices of a right triangle. (10, -4),... (answered by Fombitz)
Determine whether triangle PQR is congruent to triangle STU given the coordinates of the... (answered by ikleyn)
The point is the third vertex of a triangle with area 28 whose other two vertices are... (answered by ikleyn)
show that the triangle whose vertices are A(3,6), B(-2,-4) and C(-5,2) is a right angled (answered by Alan3354)
Determine whether the given coordinates are the vertices of a triangle. 1. A(3,5),... (answered by richwmiller,Edwin McCravy)
Square QRST has vertices Q(2,8),R(-4,8),S(-4,2),and T(2,2).Triangle QTU shares 2 vertices (answered by KMST)
rotate Triangle QRS with vertices Q( -9, -4) R (-3,-2) and S (0,0) 90 degrees in the... (answered by Fombitz)
find the length of the shortest side of the triangle whose vertices are R(-2,-1), S(1,3)... (answered by Alan3354)