Point A in the xy-coordinate system is shown below. Given

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Magoosh



Point A in the xy-coordinate system is shown below. Given two other points B (4a, b) and C (2a, 5b), what is the area of triangle ABC in terms of a and b?

A. 7ab/2
B. 9ab/2
C. 15ab/2
D. 4ab
E. 6ab

OA E

[deloitte247]

Coordinates of the vertices of the
$$\triangle ABC$$
$$\left[A\left(a,b\right)\right]\left[B\left(4a,b\right)\right]\left[C\left(2a,5b\right)\right]$$
$$Area\ of\ Trianle=\frac{1}{2}\cdot b\cdot h$$
Since position of y is constant
Base = AB = 4a - a = 3a
Distance between point C and intersection point of height with base, since x position remains constant.
Subtracting the position of the two points will provides us with the height.
Height = 5b - b =4b
Recall that area of triangle
$$\frac{1}{2}\cdot b\cdot h$$
$$\frac{1}{2}\cdot3a\cdot4b$$
$$\frac{12ab}{2}=6ab$$

$$answer\ s\ Option\ E$$

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Hi All,

We're told that Point A is in the xy-coordinate system as shown - and that two other points B (4a, b) and C (2a, 5b) are also in the system. We're asked for the AREA of triangle ABC in terms of a and b. This question can be approached in a couple of different ways, including by TESTing VALUES.

IF...
a = 1, b = 1, then the three co-ordinates are....
(1,1), (4, 1) and (2, 5)

This means that the 'base' of the triangle is 3 (it's the distance between (1,1) and (4,1) and the 'height' is 4 (it's the distance between (2,5) and the 'base'). Thus, the area of the triangle is...

Area = (1/2)(base)(height) = (1/2)(3)(4) = 6

Thus, we're looking for an answer that equals 6 when a=1 and b=1. There's only one answer that matches...

Final Answer: E

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