Question 10 - CBSE Class 10 Sample Paper for 2018 Boards

Last updated at Sept. 14, 2018 by Teachoo

If (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5
x
+ 3
y
+ 2 = 0 passes through the point (–1, 3p).

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

Question 10
If (1, /3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5x + 3y + 2 = 0 passes through the point ( 1, 3p).
Let A(2, 0), B(0, 2/9)
and let mid-point be C (1, /3)
Finding coordinates of C
(1, /3) = ((2 + 0)/2 , (0 + 2/9)/2)
(1, /3) = (2/2 ,2/9 1/2)
(1, /3) = (1 ,1/9)
Comparing y-coordinate
/3 = 1/9
= 3/9 = /
We need to show that line 5x + 3y + 2 = 0 passes through ( 1, 3p)
Point = ( 1, 3p) = ( 1, 3 1/3) = ( 1, 1)
Putting ( 1, 1) in line
5x + 3y + 2 = 0
5( 1) + 3(1) + 2 = 0
5 + 3 + 2 = 0
5 + 5 =0
0 = 0
Which is true
Hence, (1, p) passes through 5x + 3y + 2 = 0

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.