cumulative review

Question

triangle def has vertices at coordinates d(1,1) e(3,4) and f(4,2) and g has coordinates (3,1) owen claims the median from point e must pass through g is he right?

Answer 1

Hi Tannis!

The median from vertex e divides the opposite side

into two equal parts. The side opposite vertex e

is df.

Find the midpoint of df to find where the median

divides df.

midpoint of df = [1/2 * (x_d+x_f), 1/2 * (y_d+y_f)]

= [1/2 * (1+4) , 1/2 * (1+2)]

= [1/2 *(5), 1/2 * (3)]

= (5/2, 3/2)

The slope of the median line is given by

y_e-y_{meddf 4 - 3/2 5/2}

m = ------------ = ------- = ---- = 5

x_e-x_{meddf 3 - 5/2 1/2}

The slope of the line connecting e to the

point g is infinite. They both share x

values of 3 (a vertical line connects the two).

Since the slopes are different, the point

g cannot fall on the median line from e

if extended past the side df.

Owen is NOT correct.