Question

15. If (15. 17). (x, y). (11, 13) and (13, 16) are four vertices of a parallelogram taken in order, then the ratio of y to x axis A) 14:13 B) 13:12 C) 12:13 D) 13:14 ​

Answer 1

Concept:

Diagonals of a paralellogram bisect each other

Mid point of a line is give by

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1} +y_{2}}{2} )$

where, the points are $(x_{1},y_{1}),\ (x_{2},y_{2})$

Given:

A paralellogram ABCD with its 4 vertices as (15, 17),  (x, y), (11, 13) and (13, 16).

To find:

We need to find the ratio of y to x;

Solution:

Given four vertices pf parallelogram

A(15,17) ,B(x,y) ,C(11,13) and D(13,16)

Since,

mid point of AC=mid point of BD

Therefore,

$(\frac{15+11}{2},\frac{17+13}{2} )=(\frac{x+13}{2},\frac{y+16}{2} )$

⇒$(13,15)=(\frac{x+13}{2},\frac{y+16}{2} )$

Therefore,

$\frac{x+13}{2}=13$

⇒$x+13=26$

⇒x=13

And,

$\frac{y+16}{2} =15$

⇒y+16=30

⇒y=30-16

⇒y=14

The ratio of y:x=14:13

Therefore the ratio is 14:13

The correct option is (A)