Question

the vertecies of a quadilateral are: (2,2), (4,6), (8,2) and (10,6). which BEST describes this quadilateral?

A. Parallelogram
B. Recatangle
C. Rhombus
D. Square

Answer 1

You can graph the points on a graph paper and figure it out.
But if you want to figure it out analytically then:
Call the vertices ABCD in order.
First step: Find the lengths: AB, BC, CD and DA.

Answer 2

thank you sooo much!!!! so i found the distance between each set of the pints so now what do i do?? @ranga

Answer 3

What are the distances? AB, BC, CD and DA?

Answer 4

AB= 4.47
BC= 5.65
CD= 4.47
DA= 8.9
im not sure if any of them are wrong. @ranga

Answer 5

A: (2,2), B:(4,6), C: (8,2) and D: (10,6)

Just realized they have tricked us by switching the naming order of the vertices.

If we look at A and C, they have the same y coordinate of 2. That means A and C are on the same horizontal line.

If we look at B and D, they have the same y coordinate of 6. That means B and D are on the same horizontal line.

So we have a 4 sided figure AC at the bottom and BD at the top and they are both horizontal lines and therefore they are parallel.

So the order of vertices is: ACDB.

So we need to find the distances AC, CD, DB and BA to find the length of the sides.

Answer 6

The quadrilateral is ACDB
A: (2,2), B:(4,6), C: (8,2) and D: (10,6)
AC = 8 - 2 = 6
CD = sqrt{ (10-8)^2 + (6-2)^2 } = sqrt(4+16) = sqrt(20)
DB =10 - 4 = 6
BA = sqrt{ (6-2)^2 + (4-2)^2 } = sqrt(16+4) = sqrt(20)

The 4 sides are not of equal length and that rules out square and rhombus.

Answer 7

We know AC and BD are horizontal lines and their slope is 0.
Let us find the slope of the line AB. A: (2,2), B:(4,6)
slope of AB = (6-2)/(4-2) = 4/2 = 2

The side AB has a slope of 2. Its is NOT a vertical side. Therefore it is NOT a rectangle.

The given points form a parallelogram. Their opposite sides are equal and parallel.

Answer 8

okay so i got
AC=6
CD=4.47
DB=6
BA=4.47

so that makes alllott of sence!! Thank You sooo Much!!!! ^^
@ranga

Answer 9

You are welcome.

For these kinds of problems, plotting it in a graph paper or a graphing calculator or even an online graphing website such as https://www.desmos.com/calculator may be the quickest way to figure out what shape the points represent.

Answer 10

ooh okay!!! Thank you thaat would be much more useful next time @ranga

Answer 11

Alright. You are welcome.