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# Given a Line Segment Ab Joining the Points A(–4, 6) and B(8, –3). Find 1) The Ratio in Which Ab is Divided by Y-axis. 2) Find the Coordinates of the Point of Intersection. 3) The Length of Ab. - ICSE Class 10 - Mathematics

#### Question

Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find

1) The ratio in which AB is divided by y-axis.

2) Find the coordinates of the point of intersection.

3) The length of AB.

#### Solution

1) Let the line segment AB be divided by the point C on the y-axis in the ratio k: 1.

Then, by section formula, the coordinates of point C are (8k - 4)/(k + 1), (-3k + 6)/(k + 1)

Since C lies on the y-axis, coordinates of C are (0, y). On comparing, we have

(8k - 4)/(k + 1) = 0 => 8k - 4 = 0 => k = 1/2

Thus, the required ratio in which AB is divided by the y-axis is 1 : 2.

2) The point of intersection of AB and the y-axis is C.

The coordinates of point C are ((8k - 4)/(k + 1), (-3k + 6)/(k + 1)) = ((8xx1/2-4)/(1/2 + ), (-3 xx 1/2 + 6)/(1/2 + 1))

 = ((4-4)/(1/2 + 1), (-3/2 + 6)/(1/2 + 1))

= (0,3)

3) By distance formula, ABsqrt((8+4)^2 + (-3 - 6)^2) = sqrt((12)^2 + (-9)^2) = sqrt225 = 15 units.

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#### APPEARS IN

2011-2012 (March) (with solutions)
Question 2.3 | 4.00 marks

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Solution Given a Line Segment Ab Joining the Points A(–4, 6) and B(8, –3). Find 1) The Ratio in Which Ab is Divided by Y-axis. 2) Find the Coordinates of the Point of Intersection. 3) The Length of Ab. Concept: Distance Formula.
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