Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store

If points P (-7, 1), Q (x, 4) and R (3, 4) are collinear and PQ=QR. Find the values of x and y.

seo-qna
Last updated date: 22nd Mar 2024
Total views: 412.5k
Views today: 7.12k
MVSAT 2024
Answer
VerifiedVerified
412.5k+ views
Hint – In this question use the concept that the ratio in which point Q divides the line segment formed by P and R will be in the ratio 1: 1 as the points are collinear.

Complete step-by-step answer:


seo images


Let P = (x1, y1) = (-7, 1)
Q = (x3, y3) = (x, 4)
R = (x2, y2) = (3, y)
Now it is given that these three points are collinear and PQ = QR therefore point Q divide the line PR in the ratio (1 : 1) so by section formula coordinates of Q are
$ \Rightarrow {x_3} = \dfrac{{m{x_2} + n{x_1}}}{{m + n}},{y_3} = \dfrac{{m{y_2} + n{y_1}}}{{m + n}}$
Here m = 1 and n = 1.
So substitute all the values in the above equation we have,
$ \Rightarrow x = \dfrac{{3 + \left( { - 7} \right)}}{{1 + 1}},4 = \dfrac{{y + 1}}{{1 + 1}}$
So on simplifying we have,
$ \Rightarrow x = \dfrac{{ - 4}}{2},8 = y + 1$
$ \Rightarrow x = - 2,y = \left( {8 - 1} \right) = 7$
Therefore x = -2 and y = 7.
So this is the required answer.

Note – Points are said to be collinear if and only if they belong to the same line. It is advised to remember the section formula and another method to solve this problem would have been the concept that if points are collinear then slopes of two pairs of points onto that line should be equal.

Recently Updated Pages