Question

Suppose △ABC has vertices A, B, and C at (−3, 0), (0, 3), and (2, 0), respectively. If median AD¯¯¯¯¯¯¯¯ is constructed such that D is the intersection of AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯, is the equation of the median AD¯¯¯¯¯¯¯¯ y=x+3?

a) True
b) False

Answer 1

After calculating, the equation of the median AD is found to be y = 0.375x + 1.125, which is not the same as y = x + 3. Therefore, the statement is False.

This correct answer is b)

Step-by-step explanation:

To determine if the equation y = x + 3 is the correct equation for the median AD in triangle △ABC with vertices A(-3, 0), B(0, 3), and C(2, 0), we first need to find the midpoint of side BC, which would be point D, the point where the median intersects BC. Then, we create an equation of the line passing through points A and D.

The midpoint D of BC with endpoints (0, 3) and (2, 0) is, D = ((0+2)/2, (3+0)/2) = (1, 1.5). Thus, point D is (1, 1.5) and we know point A is (-3, 0).

To find the slope of line AD, which is the median, we use the formula m = (y2 - y1) / (x2 - x1). This gives us m = (1.5 - 0) / (1 - (-3)) = 1.5 / 4 = 0.375. With point A(-3, 0) we use the point-slope formula, which is y - y1 = m(x - x1), so the equation is y - 0 = 0.375(x - (-3)) or y = 0.375x + 1.125.

This equation is not the same as y = x + 3; hence the answer to the question is False.

This correct answer is b)