Question

Extended Response

6. The coordinates of the vertices of parallelogram RSTU are R(0, 0), S(2, 3), T(6, 3), and U(4, 0). What are the coordinates of the vertices of Ry=x(RSTU)?

Answer 1

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

`(y-3)/(x-2)= (3-3)/(6-3)\\(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).