(A) In a parallelogram,the diagonals bisect each other. This means the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.Midpoint

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) In a parallelogram,the diagonals bisect each other. This means the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.Midpoint of $AC = ((-2+x)/2, (1+3)/2) = ((-2+x)/2, 2)$.Midpoint of $BD = ((1+1)/2, (0+y)/2) = (1, y/2)$.Equating the coordinates of the midpoints:$(-2+x)/2 = 1 \implies -2+x = 2 \implies x = 4$.$y/2 = 2 \implies y = 4$.Therefore,the values are $x=4$ and $y=4$.

Class 10 Mathematics Coordinate Geometry Mix Examples - Coordinate Geometry

Medium

If $A(-2, 1)$,$B(1, 0)$,$C(x, 3)$,and $D(1, y)$ are the vertices of a parallelogram $ABCD$,then find the values of $x$ and $y$.

A
$x=4, y=4$
B
$x=4, y=2$
C
$x=2, y=4$
D
$x=2, y=2$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Coordinate Geometry

Subtopic

Mix Examples - Coordinate Geometry

If $P(at^{2}, 2at)$,$Q(\frac{a}{t^{2}}, \frac{-2a}{t})$ and $S(a, 0)$ are three points,show that $\frac{1}{SP} + \frac{1}{SQ}$ is independent of $t$.

Difficult

View Solution

If the point $A (2, -4)$ is equidistant from $P (3, 8)$ and $Q (-10, y)$,find the values of $y$. Also,find the distance $PQ$.

Difficult

View Solution

The point on the $Y-$ axis which is equidistant from $P(3,2)$ and $Q(-1,-5)$ is $\ldots \ldots \ldots \ldots$

Medium

View Solution

If $G$ is the centroid of a triangle having vertices $A(3h, 3k)$,$B(-3a, 0)$,and $C(3a, 0)$,then prove that $AB^2 + BC^2 + AC^2 = 3(GA^2 + GB^2 + GC^2)$.

Difficult

View Solution

The vertices of $\Delta PQR$ are $P(2, 3), Q(2, 5)$ and $R(2+\sqrt{3}, 4)$. Then $\Delta PQR$ is a $\dots$ triangle.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $A(-2, 1)$,$B(1, 0)$,$C(x, 3)$,and $D(1, y)$ are the vertices of a parallelogram $ABCD$,then find the values of $x$ and $y$.

Similar Questions

If $P(at^{2}, 2at)$,$Q(\frac{a}{t^{2}}, \frac{-2a}{t})$ and $S(a, 0)$ are three points,show that $\frac{1}{SP} + \frac{1}{SQ}$ is independent of $t$.

If the point $A (2, -4)$ is equidistant from $P (3, 8)$ and $Q (-10, y)$,find the values of $y$. Also,find the distance $PQ$.

The point on the $Y-$ axis which is equidistant from $P(3,2)$ and $Q(-1,-5)$ is $\ldots \ldots \ldots \ldots$

If $G$ is the centroid of a triangle having vertices $A(3h, 3k)$,$B(-3a, 0)$,and $C(3a, 0)$,then prove that $AB^2 + BC^2 + AC^2 = 3(GA^2 + GB^2 + GC^2)$.

The vertices of $\Delta PQR$ are $P(2, 3), Q(2, 5)$ and $R(2+\sqrt{3}, 4)$. Then $\Delta PQR$ is a $\dots$ triangle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module