. Given points A(1, 5), B(-3, 7) and C(15, 9).
(i) Find the equation of a line passing through the mid-point of AC and the point B.
(ii) Find the equation of the line through C and parallel to AB
iii) The lines obtained in parts (i) and (ii) above, intersect each other at a point P. Find
the co-ordinates of the point P.
Answers
Given : points A(1, 5), B(-3, 7) and C(15, 9).
To Find :
the equation of a line passing through the mid-point of AC and the point B.
equation of the line through C and parallel to AB
Solution:
A(1, 5) and C(15, 9).
Mid point of A and C = ( 1 + 15)/2 , ) (5 + 9)/2
= 8 , 7
B(-3, 7)
(8 , 7)
slope = 0
y - 7 = 0 (x - 8)
=> y = 7
y = 7 is the equation of a line passing through the mid-point of AC and the point B.
equation of the line through C and parallel to AB
A(1, 5) B(-3, 7)
Slope = (7 - 5)/(-3 - 1) = 2/(-4) = -1/2
C(15, 9).
y - 9 = (-1/2)(x - 15)
=> 2y - 18 = -x + 15
=> x + 2y = 33
y = 7
x + 2y = 33
=> x = 19
( 19 , 7)
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ANSWER ⤵️
Given : points A(1, 5), B(-3, 7) and C(15, 9).
To Find :
the equation of a line passing through the mid-point of AC and the point B.
equation of the line through C and parallel to AB
Solution:
A(1, 5) and C(15, 9).
Mid point of A and C = ( 1 + 15)/2 , ) (5 + 9)/2
= 8 , 7
B(-3, 7)
(8 , 7)
slope = 0
y - 7 = 0 (x - 8)
=> y = 7
y = 7 is the equation of a line passing through the mid-point of AC and the point B.
equation of the line through C and parallel to AB
A(1, 5) B(-3, 7)
Slope = (7 - 5)/(-3 - 1) = 2/(-4) = -1/2
C(15, 9).
y - 9 = (-1/2)(x - 15)
=> 2y - 18 = -x + 15
=> x + 2y = 33
y = 7
x + 2y = 33
=> x = 19
( 19 , 7)