Find the ratio in which the line joining (-2, 5) and (-5, -6) is divided by the line

y = -3. Hence find the point of intersection. 

Asked by lovetopper_121 | 14th Feb, 2020, 02:42: AM

Expert Answer:

Let the line y = -3 divides the line joining the points (-2, 5) and (-5, -6) in the ratio k:1 at point (x, y).
Since the line dividing is y=-3, therefore P will be (x, -3)
Therefore, using section formula we have
x space equals space fraction numerator k left parenthesis negative 5 right parenthesis plus 1 left parenthesis negative 2 right parenthesis over denominator k plus 1 end fraction space space a n d space space minus 3 equals fraction numerator k left parenthesis negative 6 right parenthesis plus 1 left parenthesis 5 right parenthesis over denominator k plus 1 end fraction
rightwards double arrow negative 3 equals fraction numerator negative 6 k plus 5 over denominator k plus 1 end fraction
rightwards double arrow negative 3 k minus 3 equals negative 6 k plus 5
rightwards double arrow 3 k equals 8
rightwards double arrow k equals 8 over 3
T h e r e f o r e comma space t h e space r a t i o space i s space 8 colon 3
A l s o comma space x equals fraction numerator begin display style 8 over 3 end style open parentheses negative 5 close parentheses minus 2 over denominator begin display style 8 over 3 end style plus 1 end fraction equals fraction numerator negative 40 minus 6 over denominator 11 end fraction equals negative 46 over 11
H e n c e comma space t h e space p o i n t space o f space i n t e r s e c t i o n space i s space open parentheses negative 46 over 11 comma space minus 3 close parentheses.

Answered by Renu Varma | 14th Feb, 2020, 10:53: AM