In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively. Find the equation of median through vertex A.

Also, find the equation of the line through vetex B and parallel to AC.

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Solution

Given, the co-ordinates of vertices A, B and C of a triangle ABC are (4, 7), (-2, 3) and (0, 1) respectively.

Let AD be the median through vertex A.

Co-ordinates of the point D are

$open parentheses fraction numerator negative 2 plus 0 over denominator 2 end fraction comma fraction numerator 3 plus 1 over denominator 2 end fraction close parentheses open parentheses negative 1 comma 2 close parentheses$

Slope of AD = $fraction numerator 2 minus 7 over denominator negative 1 minus 4 end fraction equals 1$

The equation of the median AD is given by:

y - y₁ = m(x - x₁)

y - 2 = 1(x + 1)

y - 2 = x + 1

y = x + 3

The slope of the line which is parallel to line AC will be equal to the slope of AC.

Slope of AC = $fraction numerator 1 minus 7 over denominator 0 minus 4 end fraction equals 3 over 2$

The equation of the line which is parallel to AC and passes through B is given by:

y - 3 = (x + 2)

2y - 6 = 3x + 6

2y = 3x + 12

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In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively. Find the equation of median through vertex A. Also, find the equation of the line through vetex B and parallel to AC.

In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively. Find the equation of median through vertex A.

Also, find the equation of the line through vetex B and parallel to AC.