sandy wrote:
In the rectangular coordinate system above, if point (a, b), shown, and the two points (4a, b) and (2a, 2b), not shown, were connected by straight lines, then the area of the resulting triangular region, in terms of a and b, would be
(A) ab/2
(B) ab
(C) 3ab/2
(D) 2ab
(E) 4ab
Here we can draw the diagram as below.
The distance between the co-ordinates (a,b) and (4a,b) is 3a, which is the base of the triangle.
We know the height of the triangle is always perpendicular to the base, so the height = 2b - b =b
Hence the Area of triangle = \(\frac{1}{2}\)* b * h = \(\frac{1}{2}\) * 3a * b =\(\frac{3ab}{2}\)
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