Area of the Triangle / Coordinate Geometry

[sukhman]

what is the area of a triangle whose vertices are the points (0,0),(1,3) and (3,3)?
A) 4.5 B)3.5 C)3 D)2.75 E)2

[DavidG@VeritasPrep]

what is the area of a triangle whose vertices are the points (0,0),(1,3) and (3,3)?
A) 4.5 B)3.5 C)3 D)2.75 E)2

Remember that the base and the height must form a 90 degree angle. If the base is the distance from 1,3 to 3,3, then BASE = 3-1 = 2. The height can be the distance from the 3,3 to the x axis, which would be 3. Height = 3-0 = 3. (remember the height doesn't have to be a side within the triangle; it just needs to be perpendicular to the base.)

If the Base = 2 and the Height = 3, then B*H/2 = 2*3/2 = 3.

See the figure below:

[Matt@VeritasPrep]

You could also find the area of the rectangle around the triangle, then subtract the two right triangles that you don't want:

Area of rectangle = 3 * 3

Area of right triangle on top = (1 * 3)/2

Area of right triangle on bottom = (3 * 3)/2

From here, (Rectangle - first ∆ - second ∆) = 9 - 1.5 - 4.5 = 3

So we're left with the triangle we want, which has an area of 3.