Question

Determine the equation of the median from J for the triangle with vertices J(2, 5), K(4, -1), and L(-2, -5).

a) y = x + 1
b) y = -x - 1
c) y = 2x + 1
d) y = -2x - 1

Answer 1

The equation of the median from vertex J to the midpoint of side KL is found using the midpoint formula and the point-slope form of a line. The calculated equation is y = 8x - 11, which does not match any of the provided choices, suggesting there might be a typo in the question.

Step-by-step explanation:

The equation of the median from vertex J in triangle JKL can be found by first calculating the midpoint M of the opposite side KL. The coordinates of K and L are (4, -1) and (-2, -5), respectively. To find the midpoint M, we compute:

M x-coordinate = (x_K + x_L)/2 = (4 + (-2))/2 = 1
M y-coordinate = (y_K + y_L)/2 = (-1 + (-5))/2 = -3

The midpoint M is therefore (1, -3). Now, we need the slope of the median, which is the slope of the line connecting J(2, 5) to M(1, -3). The slope m is calculated as follows:

m = (y_M - y_J) / (x_M - x_J) = (-3 - 5) / (1 - 2) = (-8) / (-1) = 8

With the slope m and one point J(2, 5), we use the point-slope form to find the equation of the median line. The equation is:

y - y_j = m(x - x_j)
y - 5 = 8(x - 2)
y = 8x - 16 + 5
y = 8x - 11

None of the given options match this equation; thus, the correct choice is not listed. Maybe there's been a typo in the question or the choices provided.