# Answer to Question #12182 in Algebra for ann

Question #12182
Find the perimeter of a rectangle if three of its vertices are (5,-2), (-3, -2), and (-3, 3). b) Find the area of a triangle whose vertices have coordinates (0, 9), (0, -4), and (5, -4). Describe what you did to solve each problem. Looking at the ordered pairs, did you see a correlation of the y-coordinate? Could you have solved this without graphing? If so, how?
a) Let&#039;s mark the given points by letters A, B and C so that their coordinates will be (5,-2), (-3, -2), and (-3, 3) respectfully. Let&#039;s find the coordinates of missing point D. It&#039;s coordinates are (5, 3). We can find them without graphing by looking through no-repeated coordinates of the given points. A and C are opposite vertices. So,

T = 2AB + 2AD = 2(5-(-3)) + 2(3-(-2)) = 26.

b) Let&#039;s apply the Heron&#039;s formula:

where

p = [a+b+c]/2

and a, b and c are the lenghts of the sides of the triangle.

a = AB = &radic;[(5-(-3))&sup2;+(-2-(-2))&sup2;] = 8;
b = BC = &radic;[(-3-(-3))&sup2;+(-2-3)&sup2;] = 5;
c = CA = &radic;[(-3-5)&sup2;+(3-(-2))&sup2;] = 9;
p = [8+5+9]/2 = 11;

and so,

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