Question

A kite has vertices R(2, 2), S(4, 0), T(2, -2), and U(-5, 0). What happens to the area of the kite when diagonal SU is multiplied by 1/3 (one-third)? (Hint: Sketch the polygon first.)

Its area is multiplied by 3.

Its area is multiplied by 1/3.

Its area is multiplied by 1/2.

Its area is multiplied by 1/9.

Answer 1

The polygon is made of two triangles RSU and STU. When u sketch the polygon u see that the diagonal SU is lying on x-axis(as y coordinate is 0).
So the base of both the triangles is SU whose length is 9. The height of the triangle RSU is the distance of point R from x-axis i.e. 2.
So area of the tri RSU becomes half X base X height =1/2 *9*2=9
Similarly area of tri STU =9.
Therefore the area of polygon=18.
Now SU=9 and 1/3 SU=3.
Repeat the whole process and u will get area of polygon =6 i.e. area has become 1/3 of the original.

Therefore area is multiplied by 1/3.

Answer 2

I must have stopped my math to early, because I got the answer of 9 . But thank you for helping me 1/3 is correct.

Answer 3

Ur welcome