Question

A(1, 2), B(4, 6) and C(8, 12) form the vertices of a triangle. Which of the following is not the coordinates of medians of triangle ABC?

• A. $(\frac{5}{2},4)$
• B. (6, 9)
• C. $(\frac{9}{2},7)$
• D. $(\frac{7}{2},4)$

Answer 1

The correct option is D $(\frac{7}{2},4)$

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

The coordinates of the midpoint of a line segment joining $(x_1,y_1)\text{and}(x_2,y_2)$ are $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}).$

Substituting values of $x_1,x_2,y_{1}and{y}_2$ , we get

Midpoint of AB = $(\frac{1+4}{2},\frac{2+6}{2})$ = $(\frac{5}{2},4)$

Midpoint of BC = $\frac{4+8}{2},\frac{6+12}{2}$ = (6, 9)

Midpoint of AC = $\frac{1+8}{2},\frac{2+12}{2}$ = $(\frac{9}{2},7)$

Therefore, the only option which is not a median of the given triangle is $(\frac{7}{2},4).$