Algebra/Geometry

Question

A line with slope equal to 1 and a line with slope equal to 2 intersect at the point (4,6). Points Q and R are both on the x-axis. What is the area of triangle PQR?

Answer 1

A line with a slope of 1 is y = x + b, use point (4,6) to find b.

6 = 4 + b, so b = 2. For this line, y = x + 2, the x intercept is where y = 0. If y = 0, then x is -2, so one end of the triangle is (-2, 0).

A line with a slope of 2 is y = 2x + b, use point (4,6) to find b.

6 = 8 + b, so b = -2. For this line, y = 2x - 2, the x intercept is where y = 0. If y = 0, then x is 1, so the other end of the triangle is (1,0).

The area of a triangle is 1/2 the base times the height. A = (1/2)bh. The base is the distance between the intercept points (-2,0) and (1,0) so 3 units. This height is 6 units, the y value of the point of intersection.

So the Area = (1/2)(3)(6) = 9 units