The coordinates of ▭WISH are given. Plot and connect the following set of points in the Cartesian Plane. Decide whether WISH is a rectangle, rhombus or a square.

Question

(a) W (-2, 3); I (-2, -4); S(2, -4); H(2, 3)

(b) W (5, 2); I (1, 9); S(-3, 2); H(1, -5)

(c) W (-4, 0); I (3, 7); S(6, 4); H(-1, -3)

(d) W (1, 1); I (-2, 4); S(-5, 1); H(-2, -2)

Answer 1

If you plot the points, you'll be able to get a pretty good idea. I plotted the first 2 problems for you:

Problem a) has right angles so must be either a rectangle or square. The side lengths are NOT all the same so it is a rectangle.

Problem b) does NOT have right angles, To find out if the side lengths are all the same, you can use the distance formula but the short cut is to make sure that when you are moving from one point to the next, you move the same way each time. In this case, you either go over 4 and up/down 7 or over 7 and up/down 4. If you can, the side lengths are the same and it's a rhombus.

Repeat on the other two problems.

Answer 2

I plotted coordinates of points given in (c) and (d) parts. I discovered that points of (c) part form a rectangle and points of (d) part form a rhombus. I verified that slopes of adjacent lines are +1 and -1 for lines joining for points of (c) part. For (d) part, I verified that side lengths are equal. I hope this helps.

Sincerely,

Shailesh (Sky) Kadakia