Question

Extended Response

Answer 1

Answer:

The Coordinate of the vertices of Parallelogram RSTU are R(0,0), S(2,3),T(6,3) and U (4,0).

we have to find the vertices of a point which cuts the side of parallelogram ST  .It is given that line y = x passes through R.

Suppose that it cuts the side ST at M (p,q).

Equation of line passing through T(6,3)and S (2,3) is

$\frac{y-3}{x-2}= \frac{3-3}{6-3}\\\frac{y-3}{x-2} = 0\\y- 3=0$

it passes through (p,q)∴

∴ q -3 =0     ...........(1)

Line y=x passes through (p,q).

p -q=0

p=q

Equation (1) becomes

p= q=3

So the line y =x cuts TU at M (3,3).