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

A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB. (i) the coordinates of A and B. (ii) the slope of the line AB. (iii) the equation of the line AB. Equation of a Straight Line, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Find :

(i) the coordinates of A and B.

(ii) the slope of the line AB.

(iii) the equation of the line AB.

Straight Line Eq

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Answer

(i) Let the coordinates of A be (x, 0) and B be (0, y).

P(2, -3) is the mid-point of AB. So we have,

2=x+02 and 3=0+y22=x2 and 3=y2x=4 and y=6.\Rightarrow 2 = \dfrac{x + 0}{2} \text{ and } -3 = \dfrac{0 + y}{2} \\[1em] \Rightarrow 2 = \dfrac{x}{2} \text{ and } -3 = \dfrac{y}{2} \\[1em] \Rightarrow x = 4 \text{ and } y = -6.

Hence. the coordinates of A are (4, 0) and B are (0, -6).

(ii) Slope of AB = y2y1x2x1\dfrac{y2 - y1}{x2 - x1}

Putting values we get slope,

=(60)(04)=64=32.= \dfrac{(-6 - 0)}{(0 - 4)} \\[1em] = \dfrac{-6}{-4} \\[1em] = \dfrac{3}{2}.

Hence, the slope of the line AB is 32.\dfrac{3}{2}.

(iii) Equation of AB will be

⇒ y - y1 = m(x - x1)
⇒ y - 0 = 32\dfrac{3}{2}(x - 4)
⇒ 2y = 3x - 12
⇒ 3x - 2y = 12.

Hence, the equation of AB is 3x - 2y = 12.

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