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27 Jul 2017, 09:17
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B
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78% (02:38) correct
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On the coordinate plane there are 3 points A(-1, 1), B(0, -2), and C(3, 4). What is the area of the triangle connecting the 3 points?
(A) 15/4
(B) 15/2
(C) 15
(D) 13/4
(E) 13/2
(A) 15/4
(B) 15/2
(C) 15
(D) 13/4
(E) 13/2
27 Jul 2017, 10:57
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Given data
x1=-1,y1=1
x2=0,y2=-2
x3=3,y3=4
Given the vertices of the triangle
Area = \(\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y1 - y3x1)|\)
Substiuting these values,
Area = \(\frac{1}{2} * |2 + 6 + 7|\) = \(\frac{1}{2} * |15| = \frac{15}{2}\)(Option B)
x1=-1,y1=1
x2=0,y2=-2
x3=3,y3=4
Given the vertices of the triangle
Area = \(\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y1 - y3x1)|\)
Substiuting these values,
Area = \(\frac{1}{2} * |2 + 6 + 7|\) = \(\frac{1}{2} * |15| = \frac{15}{2}\)(Option B)
27 Jul 2017, 11:22
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ammuseeru
Attachment:
tri.area.grid.rectangle.jpg [ 37.89 KiB | Viewed 44736 times ]
Because this triangle has no vertical or horizontal leg, plot its three coordinates, connect them, then draw a rectangle around the triangle (see diagram).
Then find area of rectangle and subtract the areas of the three yellow triangles, whose areas are easy to find because they are right triangles (their legs are base and height).
1. (Area of rectangle) - (area of OTHER triangles) = area of THIS triangle
Area of rectangle = (L * W)
L = 6 (count on the graph, or subtract y-coordinates at points B and C)
W = 4 (count, or subtract x-coordinates at points A and B)
Rectangle area = 24
2. Find area of three triangles (yellow) ABX, BCY, and DXY (coordinates are in red - find base and height for each by counting or subtracting x- and then y-coordinates)
Area of triangle ABX = \(\frac{1}{2} b*h =\\
\frac{(3*4)}{2}\) = 6
Area of triangle BCY = \(\frac{(6 * 3)}{2}\) = 9
Area of triangle DXY = \(\frac{(1*3)}{2} = \frac{3}{2}\)
Total area of yellow triangles = 6 + 9 + \(\frac{3}{2}\) = \(\frac{33}{2}\)
3. (Rectangle area) - (total area of 3 yellow triangles) =
area of THIS triangle
24 - \(\frac{33}{2}\) =
\(\frac{48}{2} - \frac{33}{2} = \frac{15}{2}\)
Answer B
Hope it helps.
