Question

In the given figure, P(0, 4) and Q(-2, y) are the points of Trisection of the line joining A(2, -3) and B(4. - 6), then A(2-3) P(O.-4) Q(-2,y) B(-4,-6) y equals​

Answer 1

Answer:

-5

Step-by-step explanation:

Q is the midpoint of PQ so,

x=0+(-4)/2

=-4/2

=-2

y=-4+(-6)/2

=-4-6/2

=-10/2

=-5

Answer 2

Lines

Given:

$P(0,-4), Q(-2, y),A(2, -3),B(-4,-6)$

P and Q are the point of trisection of line AB.

To find:

Value of y.

Explanation:

The coordinates of mid point will divide a line segment into 2 equal parts, here there are 2 point which divides the line segment AB in 3 equal parts.

We use midpoint formula to find the coordinates of the midpoint of the given line.

AP, PQ and QB are the three equal parts. So, we can find the midpoint of AQ which will be equal to the co-ordinates of P.

So,

$x_{1} =2\\x_{2} =-2\\y_{1} =-3\\y_{2} =y$

$m:n=1:1$

By mid-point formula,

$(0,-4)=(\frac{(x1 + x2)}{2} ,\frac {(y1 + y2)}{2})$

$(0,-4)=(\frac{(2 + (-2))}{2} ,\frac {(-3+ y)}{2})$

$-4=\frac{-3+y}{2} \\=>-8=-3+y\\=>-5=y$

So, the value of y is (-5).

We could have also used the point P, Q, B to find the value of y.