C is the mid-point of PQ. If P is (4, x), C is (y, -1) and Q is (-2, 4), then x and y respectively are ___________.

- 6 and 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

-6 and 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 and -1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 and -2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A - 6 and 1
Given points are P(4, x), Q(-2, 4) and mid-point is C(y-1)
$∵$ Mid point (x, y) of the line joining the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is x = $(\frac{x_{2} + x_{1}}{2})$ and y = $(\frac{y_{2} + y_{1}}{2})$
$∴ \frac{4 - 2}{2} = y a n d \frac{4 + x}{2} = - 1$
$\Rightarrow y = 1 a n d x = - 6$

Suggest Corrections

Similar questions

Q. The plane

\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1

meets the coordinate axes at A, B, C respectively. D and E are the mid-points of AB and AC respectively. Coordinates of the mid-point of DE are

Q. If A and B are the sums of odd and even terms respectively in the expansion of (x + a)ⁿ, then (x + a)²ⁿ − (x − a)²ⁿ is equal to
(a) 4 (A + B)
(b) 4 (A − B)
(c) AB
(d) 4 AB

IN the figure, PQRS is a parallelogram. If X and Y are mid points of PQ and SR respectively and diagonal SQ is joined, the ratio $a r (| | g m X Q R Y) : a r (△ Q S R)$ =

Q. ABCD is a parallelogram and X, Y are the mid-points of sides AB and Cd respectively. Then quadrilateral AXCY is a :

The figure shows a parallelogram PQRS, in which, A is the mid point of PQ and B is the mid point of RS.

S1 : SX = XY

S2 : XY = QY

Join BYJU'S Learning Program

C is the mid-point of PQ. If P is (4, x), C is (y, -1) and Q is (-2, 4), then x and y respectively are ___________.

The correct option is A - 6 and 1Given points are P(4, x), Q(-2, 4) and mid-point is C(y-1) ∵ Mid point (x, y) of the line joining the points (x1,y1) and (x2,y2) is x = (x2+x12) and y = (y2+y12) ∴4−22=y and 4+x2=−1 ⇒y=1 and x=−6