A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the

(i) co-ordinates of A and B

(ii) slope of line AB

(iii) equation of line AB.

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Solution

(i) Let the co-ordinates be A(x, 0) and B(0, y).

Mid-point of A and B is given by $open parentheses fraction numerator x plus 0 over denominator 2 end fraction comma fraction numerator y plus 0 over denominator 2 end fraction close parentheses equals open parentheses x over 2 comma y over 2 close parentheses$

(ii) Slope of line AB, m = $fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator negative 6 minus 0 over denominator 0 minus 4 end fraction equals 3 over 2$

(iii) Equation of line AB, using A(4, 0)

2y = 3x - 12

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The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :

(i) the equation of AB;

(ii) the co-ordinates of the point where the line AB intersects the y-axis.

A line AB meets X-axis at A and Y-axis at B. P(4, -1) divides AB in the ratio 1 : 2.

(i) Find the co-ordinates of A and B.

(ii) Find the equation of the line through P and perpendicular to AB.

3 x - 4 y + 12 = 0

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