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ICSE Class 10 Answered

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 the y axis. 2) the coordinates of the points of intersection.  3) the length AB.
Asked by murmusweetie215 | 06 Dec, 2018, 05:36: AM
answered-by-expert Expert Answer
If Y-axis divides the given line AB, then coordinates of  the point C which divides the given line
in the ratio l : m is (0,y) . Since the point C is in Y-axis, its x-coordinate is zero.
 
we have the formula for the point (xp, yp ) which divides the line joining points (x1 , y1) and (x2 , y2)
in the ratio l : m as given below
 
begin mathsize 12px style x subscript p space equals space fraction numerator m space x subscript 1 space plus space l space x subscript 2 over denominator l plus m end fraction space semicolon space space space space space space space y subscript p space equals space fraction numerator m space y subscript 1 space plus space l space y subscript 2 over denominator l plus m end fraction space end style
since x-coordinate of point C is zero, we have,   -4m + 8l = 0  or   l/m = 1/2
 
Hence point C divides the line AB in the ratio 1 : 2
 
y-coordinate of C = (2×6 - 1×3)/(1+2) = 3 
 
Hence coordinates of point C is ( 0, 3)
 
length of AB = begin mathsize 12px style square root of open parentheses negative 4 minus 8 close parentheses squared plus open parentheses 6 plus 3 close parentheses squared end root space equals space 15 end style
Answered by Thiyagarajan K | 06 Dec, 2018, 08:44: AM

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