Question:
The line joining $A (2, -7)$ and $B(6, 5)$ is divided into $4$ equal parts by the points $ P,Q$ and $R$ such that $AQ = RP = QB$. The midpoint of $ PR$ is _______
The line joining $A (2, -7)$ and $B(6, 5)$ is divided into $4$ equal parts by the points $ P,Q$ and $R$ such that $AQ = RP = QB$. The midpoint of $ PR$ is _______
Updated On: May 17, 2024
- (4,-1)
- (8,-2)
- (4,12)
- (-8,1)
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The Correct Option is A
Solution and Explanation
Given that,
$A P=P Q=Q R=R B$
and $A Q=R P=Q B$
Since, $A Q=Q B$, that means $Q$ is the mid point of
$A B=\left[\frac{2+6}{2}, \frac{-7+5}{2}\right]=(4,-1)$
Mid point of $P R=(4,-1)$
$[\because P Q=Q R]$
$A P=P Q=Q R=R B$
and $A Q=R P=Q B$
Since, $A Q=Q B$, that means $Q$ is the mid point of
$A B=\left[\frac{2+6}{2}, \frac{-7+5}{2}\right]=(4,-1)$
Mid point of $P R=(4,-1)$
$[\because P Q=Q R]$
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Concepts Used:
Distance of a Point From a Line
The length of the perpendicular drawn from the point to the line is the distance of a point from a line. The shortest difference between a point and a line is the distance between them. To move a point on the line it measures the minimum distance or length required.
To Find the Distance Between two points:
The following steps can be used to calculate the distance between two points using the given coordinates:
- A(m1,n1) and B(m2,n2) are the coordinates of the two given points in the coordinate plane.
- The distance formula for the calculation of the distance between the two points is, d = √(m2 - m1)2 + (n2 - n1)2
- Finally, the given solution will be expressed in proper units.
Note: If the two points are in a 3D plane, we can use the 3D distance formula, d = √(m2 - m1)2 + (n2 - n1)2 + (o2 - o1)2.
Read More: Distance Formula