IXL - Classify shapes on the coordinate plane: justify your answer (Geometry practice)

The graph shows quadrilateral

a parallelogram? Justify your answer.

Yes,

is parallel to

and

is parallel to

Yes,

is parallel to

and

is parallel to

No,

is not parallel to

No,

is not parallel to

ref_doc_title.

Learn with an example

question

The graph shows quadrilateral

an isosceles trapezoid? Justify your answer.

Yes,

is parallel to

and

is congruent to

Yes,

is parallel to

and

is congruent to

No, none of the sides are parallel.

No, none of the sides are congruent.

key idea

These formulas can help you classify shapes on a coordinate plane:

Distance formula:
d
=
(
x
2
–
x
1
)
2
+
(
y
2
–
y
1
)
2
Midpoint formula:
M
=
i
x
1
+
x
2
2
,
y
1
+
y
2
2
i
Slope formula:
m
=
y
2
–
y
1
x
2
–
x
1

solution

The graph shows quadrilateral

It has vertices at

(

)

(

–

)

(

–

)

and

(

–

)

To justify whether

is an isosceles trapezoid or not, you can use the properties of an isosceles trapezoid.

In an isosceles trapezoid, one pair of opposite sides are parallel and the other pair of opposite sides are congruent. So, to determine whether

has a pair of congruent sides, you can first find the length of each side.

(

–

)

(

–

)

(

–

)

(

–

(

–

)

104

(

–

(

–

)

(

–

(

–

)

(

–

)

(

–

)

Since none of the sides have the same side length, none of the sides are congruent.

So, this statement justifies why

is not an isosceles trapezoid:

green checkmark, No, none of the sides are congruent.

These statements are not correct:

red X symbol, Yes, is parallel to , and is congruent to .

is not parallel to , and is not congruent to , so this statement is false.

red X symbol, Yes, is parallel to , and is congruent to .

is not congruent to , so this statement is false.

red X symbol, No, none of the sides are parallel.

is parallel to , so this statement is false.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

O.2Classify quadrilaterals I

F.1Classify triangles

E.4Slopes of parallel and perpendicular lines

B.13Distance formula

B.6Midpoints

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