Question

The equation of the median through A of a triangle ABC whose vertices are A(1, 4), B(2, -3) and C(-1, -2) is plzz urgent ~ - ~ the answer is 13x - y - 9 = 0 plzz i need steps

Answer 1

Answer:

Step-by-step explanation:

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

- Coordinates of the midpoint are (($x_{1}$ + $x_{2}$) / 2 , ($y_{1}$ + $y_{2}$) / 2)

- Formula of the slope of a line is m = ( $y_{2}$ - $y_{1}$ ) / ( $x_{2}$ - $x_{1}$ )

- Point-slope form for linear equation is (y - $y_{1}$) = m(x - $x_{1}$)

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Coordinates of midpoint of BC are ( $\frac{-1+2}{2}$ , $\frac{-2-3}{2}$ ) = ( $\frac{1}{2}$ , $\frac{-5}{2}$ )

The slope of the median passing through A(1, 4) and (0.5, - 2.5)

m = $\frac{-2.5-4}{0.5-1}$ = 13

y - 4 = 13(x - 1)

y = 13x - 9 (slope-intercept form)

13x - y - 9 = 0 (standard form)