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Question
Given a line segment AB joining the points A (- 4, 6) and B (8, – 3). Find:
(i) the ratio in which AB is divided by the y- axis.
(ii) find the ordinates of the point of intersection.
(iii) the length of AB.
Graph
Sum
Solution
A(-4, 6), B(8, -3)
Let ratio be k: 1
(i) Where the y-axis divide AB, x = 0
∴ x = `(m_1x_2 + m_2x_1)/(m_1 + m_2)`
∴ 0 = `(k xx 8 + 1 xx (-4))/(k + 1)`
⇒ 8k - 4 = 0
⇒ 8k = 4
⇒ k = `(4)/(8) = (1)/(2)`
So, ratio be 1: 2
(ii) Now, y = `(1 xx (-3) + 2 xx 6)/(1 + 2)`
= `(-3 + 12)/(3)` = 3
So, point of intersection (0, 3)
(iii) AB = `sqrt((8 + 4)^2 + (-3 - 6)^2)`
= `sqrt((12)^2 + (-9)^2)`
= `sqrt(144 + 81) = sqrt(225)`
= 15 units.
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Geometric Understanding of c as the y-intercept Or the Ordinate of the Point Where the Line Intercepts the y Axis Or the Point on the Line Where x=0
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