In the following diagram, write down :

(i) the co-ordinates of the points A, B and C.

(ii) the equation of the line through A and parallel to BC.

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Solution

(i) The co-ordinates of points A, B and C are (2, 3), (-1, 2) and (3, 0) respectively.

(ii) Slope of BC = $fraction numerator 0 minus 2 over denominator 3 plus 1 end fraction equals fraction numerator negative 2 over denominator 4 end fraction equals fraction numerator negative 1 over denominator 2 end fraction$

Slope of a line parallel to BC = Slope of BC = $fraction numerator negative 1 over denominator 2 end fraction$

Required equation of a line passing through A and parallel to BC is given by

y - y₁ = m(x - x₁)

y - 3 = $fraction numerator negative 1 over denominator 2 end fraction$ (x - 2)

2y - 6 = -x + 2

x + 2y = 8

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In the following diagram, write down : (i) the co-ordinates of the points A, B and C. (ii) the equation of the line through A and parallel to BC.

(i) The co-ordinates of points A, B and C are (2, 3), (-1, 2) and (3, 0) respectively. (ii) Slope of BC = Slope of a line parallel to BC = Slope of BC = Required equation of a line passing through A and parallel to BC is given by y - y1 = m(x - x1) y - 3 = (x - 2) 2y - 6 = -x + 2 x + 2y = 8

In the following diagram, write down :

(i) the co-ordinates of the points A, B and C.

(ii) the equation of the line through A and parallel to BC.