Name:
Date:
Page 1 of 3
Activity 2.4.2 Kites in the Coordinate Plane
A kite is a quadrilateral with two pairs of adjacent sides congruent . You can use the coordinates
of the vertices of a quadrilateral and the distance formula to determine whether or not a
quadrilateral is a kite.
If you come to the conclusion that a figure is a kite, then you can test the slopes of the diagonals
of the kite to see what relationship is formed. In the questions below you will use the distance
formula to determine whether or not the figure is a kite.
Here are some formulas you may want to recall:
Distance formula = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Slope formula =
(𝑥2 −𝑥1 )
(𝑦2− 𝑦1 )
Slopes of parallel lines are equal.
Slopes of perpendicular lines are the opposite reciprocals of each other. For example lines with
slopes -5 and
1
5
are perpendicular; therefore two lines with these slopes create a right angle.
1. Plot the vertices of quadrilateral OBCD and find the lengths of each side using the distance
formula.
For all problems below:
a. Leave answers exact in square root form if necessary. (For example: √37 )
𝑂(0,0), 𝐵(2,4), 𝐶(4,4), 𝐷(4,2)
OB = ______________
OD = ______________
BC = ______________
DC = ______________
10
b. Which pairs of sides are congruent?
8
6
c. Are these pairs of sides adjacent?
4
2
d. Is OBCD a kite? Explain.
-10
-8
-6
-4
-2
2
4
6
-2
e. Does OBCD have any lines of symmetry?
If so, draw them on the figure.
-4
-6
-8
-10
Activity 2.4.2
Connecticut Core Geometry Curriculum Version 1.0
8
10
Name:
Date:
Page 2 of 3
̅̅̅̅ 𝑎𝑛𝑑 𝐵𝐷.
̅̅̅̅̅
e. Find the slopes of 𝑂𝐶
Slope of OC = ________________
Slope of BD = ________________
̅̅̅̅ 𝑎𝑛𝑑 𝐵𝐷
̅̅̅̅ ? ______________________________________
f. What is the relationship between 𝑂𝐶
2. Draw quadrilateral QUAD with the given vertices. Then classify the quadrilateral by finding
the length of the sides using the distance formula.
𝑄(0,0), 𝑈(4,0), 𝐴(3,6), 𝐷(−1,6)
QU = ______________
AU = ______________
DA = ______________
DQ = ______________
B Which pairs of sides are congruent?
10
c. Are these pairs of sides adjacent?
8
6
4
d. Is OBCD a kite? Explain.
2
-10
e. Find the slopes of the four sides.
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
f. Classify QUAD. ___________________
Explain your reasoning.
-10
g. Are there any lines of symmetry?______
If so, draw them on the figure.
̅̅̅̅̅
̅̅̅̅𝑎𝑛𝑑 𝐴𝑄.
h. Find the slopes of 𝐷𝑈
̅̅̅̅ = ________________
Slope of 𝐷𝑈
̅̅̅̅ = ________________
Slope of 𝐴𝑄
̅̅̅̅? ______________________________________
̅̅̅̅𝑎𝑛𝑑 𝐴𝑄
i. What is the relationship between 𝐷𝑈
Activity 2.4.2
Connecticut Core Geometry Curriculum Version 1.0
Name:
Date:
Page 3 of 3
3. Draw quadrilateral POLY with the given vertices. Then classify the quadrilateral by finding
the length of the sides using the distance formula.
𝑃(−3,0), 𝑂(0,3), 𝐿(3,0), 𝑌(0, −3)
PO = ______________
LO = ______________
PY = ______________
LY = ______________
10
b. Classify POLY Explain your reasoning.
8
c. Are there other ways to classify POLY?
Explain.
6
d. Are there any lines of symmetry?______
If so, draw them on the figure.
2
4
-10
-8
-6
-4
-2
2
4
6
-2
̅̅̅̅𝑎𝑛𝑑 𝑃𝐿.
̅̅̅̅
e. Find the slopes of 𝑂𝑌
-4
-6
Slope of ̅̅̅̅
𝑂𝑌 = ________________
-8
Slope of ̅̅̅̅
𝑃𝐿 = ________________
-10
f. What is the relationship between ̅̅̅̅
𝑂𝑌𝑎𝑛𝑑 ̅̅̅̅
𝑃𝐿?
______________________________________
Conclusions:
a. After completing the activity, we can see that in kites, the diagonals are
____________________.
b. In a kite, we can also see that the line of symmetry is also a ____________________.
c. We also saw that a _________________ is a type of kite.
d. Two pairs of adjacent sides of a kite are _____________________.
Activity 2.4.2
Connecticut Core Geometry Curriculum Version 1.0
8
10