In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find :

(i) equation of line AB.

(ii) equation of line CD.

(iii) co-ordinates of points E and D.

Open in App

Solution

$left parenthesis i right parenthesis space e q u a t i o n space o f space l i n e space A B. space space g i v e n space A left parenthesis 0 comma 6 right parenthesis space a n d space B left parenthesis negative 6 comma 8 right parenthesis t h e n comma space s l o p e space equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator 8 minus 6 over denominator negative 6 minus 0 end fraction equals fraction numerator 2 over denominator negative 6 end fraction equals negative 1 third e q u a t i o n space o f space a space l i n e space colon space space y minus y subscript 1 equals m left parenthesis x minus x subscript 1 right parenthesis rightwards double arrow y minus 6 equals negative 1 third open parentheses x minus 0 close parentheses rightwards double arrow 3 y minus 18 equals negative x rightwards double arrow x plus 3 y minus 18 equals 0 space space space space left parenthesis e q u a t i o n space o f space A B right parenthesis left parenthesis i i right parenthesis space e q u a t i o n space o f space l i n e space C D. l i n e space C D space i s space p e r p e n d i c u l a r space t o space A B semicolon apostrophe s l o p e space o f space C D space equals fraction numerator negative 1 over denominator s l o p e space A B end fraction equals fraction numerator negative 1 over denominator open parentheses negative 1 third close parentheses end fraction equals 3 C D space p a s sin g space t h r o u g h space C left parenthesis 2 comma 10 right parenthesis space a l s o comma t h e n space colon e q u a t i o n space C D space rightwards double arrow y minus y subscript 1 equals m left parenthesis x minus x subscript 1 right parenthesis y minus 10 equals 3 left parenthesis x minus 2 right parenthesis y minus 10 equals 3 x minus 6 3 x minus y plus 4 equals 0 space space space space left parenthesis e q u a t i o n space o f space C D right parenthesis left parenthesis i i i right parenthesis space c o minus o r d i n a t e s space o f space p o i n t s space E space a n d space D. T h e space p o i n t space E space i s space t h e space x minus i n t e r c e p t space o f space l i n e space A B colon s o comma space p u t space y equals 0 space i n space l i n e space e q u a t i o n space o f space A B rightwards double arrow x plus 3 y minus 18 equals 0 space space rightwards double arrow x plus 3 cross times 0 minus 18 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow x equals 18 s o bold comma bold space bold italic p bold italic o bold italic i bold italic n bold italic t bold space bold italic E bold equals bold left parenthesis bold 18 bold comma bold 0 bold right parenthesis bold italic S bold italic i bold italic m bold italic i bold italic l bold italic i bold italic a bold italic r bold italic l bold italic y bold comma space T h e space p o i n t space D space i s space x minus i n t e r c e p t space o f space t h e space l i n e space C D s o comma space p u t space y equals 0 space i n space l i n e space e q u a t o n space o f space C D rightwards double arrow 3 x minus y plus 4 equals 0 space space space rightwards double arrow space 3 x minus 0 plus 4 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space 3 x equals negative 4 space space rightwards double arrow space x equals negative 4 over 3 bold italic s bold italic o bold comma space bold italic p bold italic o bold italic i bold italic n bold italic t bold space bold italic D bold space bold equals open parentheses bold minus bold 4 over bold 3 bold comma bold 0 close parentheses space$

Suggest Corrections

Similar questions

A line AB meets X-axis at A and Y-axis at B. P(4, -1) divides AB in the ratio 1 : 2.

(i) Find the co-ordinates of A and B.

(ii) Find the equation of the line through P and perpendicular to AB.

Q. Answer the questions with the help of the fig. 5.36

(i) Write the name of the line having equation y = 4
(ii) Write the co-ordinates of the point of intersection of line AB and line MN.
(iii) What is the equation of line EF?
(iv) Write the equations of line MN, line PQ, line AB and line CD.

Figure

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

(i) co-ordinates of A and B

(ii) slope of line AB

(iii) equation of line AB.

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :

(i) the equation of AB;

(ii) the co-ordinates of the point where the line AB intersects the y-axis.

A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects the co-ordinates axes at points A and B. M is the mid-point of the segment AB. Find :

(i) The equation of the line.

(ii) The co-ordinates of A and B.

(iii) The co-ordinates of M.

Join BYJU'S Learning Program

In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find : (i) equation of line AB. (ii) equation of line CD. (iii) co-ordinates of points E and D.

In the given figure, line AB meets y-axis at point A. Line through C(2, 10) and D intersects line AB at right angle at point P. Find :

(i) equation of line AB.

(ii) equation of line CD.

(iii) co-ordinates of points E and D.