Name: ________________________ Class: ___________________ Date: __________
ID: A
Distance Formula Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find CD and EF. Then determine if CD ≅ EF .
b.
CD =
CD =
13 , EF = 13 , CD ≅ EF
5 , EF = 13 , CD ≅/ EF
c.
CD =
13 , EF = 3 5 , CD ≅/ EF
d.
CD =
5 , EF =
a.
____
5 , CD ≅ EF
2. Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from
T(4, –2) to U(–2, 3).
a. –1.0 units
b. 3.4 units
c. 0.0 units
d. 7.8 units
1
Name: ________________________
____
ID: A
3. There are four fruit trees in the corners of a square backyard with 30-ft sides. What is the distance between
the apple tree A and the plum tree P to the nearest tenth?
a.
b.
c.
d.
42.4 ft
42.3 ft
30.0 ft
30.3 ft
2
ID: A
Distance Formula Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
Step 1 Find the coordinates of each point.
C(0, 4), D(3, 2) , E(−2, 1) , and F(−4, − 2)
Step 2 Use the Distance Formula.
d =
CD =
(x 2 − x 1 ) 2 + (y 2 − y 1 ) 2
2
(3 − 0) + (2 − 4)
=
3 2 + (−2)
=
9+4 =
2
EF =
2
13
(−4 − (−2)) 2 + (−2 − 1)
2
=
(−2) + (−3)
=
4+9 =
2
2
13
Since CD = EF , CD ≅ EF .
Feedback
A
B
C
D
Correct!
The square of a negative number is positive.
Subtracting a negative number is the same as adding the number. –(–2) = 2.
Use the distance formula after finding the coordinates of each point.
PTS:
OBJ:
LOC:
KEY:
1
DIF: Average
REF: 1955020a-4683-11df-9c7d-001185f0d2ea
1-6.3 Using the Distance Formula STA: NY.NYLES.MTH.05.GEO.G.G.67
MTH.C.11.05.04.008
TOP: 1-6 Midpoint and Distance in the Coordinate Plane
coordinate geometry | distance | congruent segments
DOK: DOK 2
1
ID: A
2. ANS: D
Method 1 Substitute the values for the
coordinates of T and U into the Distance
Formula.
Method 2 Use the Pythagorean Theorem.
Plot the points on a coordinate plane. Then
draw a right triangle.
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2
1¯
1¯
Ë 2
Ë 2
TU =
2
=
(−2 − 4) + (3 − −2)
=
(−6) + (5)
=
61
2
2
2
≈ 7.8 units
Count the units for sides a and b. a = 6 and
b = 5. Then apply the Pythagorean Theorem.
c 2 = a 2 + b 2 = 62 + 5 2 = 36 + 25 = 61
c ≈ 7.8 units
Feedback
A
B
C
D
The distance is the square root of the quantity (x2 − x1)^2 + (y2 − y1)^2.
The distance is the square root of the quantity (x2 − x1)^2 + (y2 − y1)^2.
The distance is the square root of the quantity (x2 − x1)^2 + (y2 − y1)^2.
Correct!
PTS:
OBJ:
STA:
LOC:
TOP:
KEY:
1
DIF: Average
REF: 19573d56-4683-11df-9c7d-001185f0d2ea
1-6.4 Finding Distances in the Coordinate Plane
NY.NYLES.MTH.05.GEO.G.G.48 | NY.NYLES.MTH.05.GEO.G.G.67
MTH.C.11.03.02.05.02.002 | MTH.C.11.05.04.008
1-6 Midpoint and Distance in the Coordinate Plane
coordinate geometry | distance | Pythagorean Theorem
DOK: DOK 2
2
ID: A
3. ANS: A
Set up the yard on a coordinate plane so that the apple tree A is at the origin, the fig tree F has coordinates
(30, 0), the plum tree P has coordinates (30, 30), and the nectarine tree N has coordinates (0, 30).
The distance between the apple tree and the plum tree is AP.
ÊÁ x − x ˆ˜ 2 + ÊÁ y − y ˆ˜ 2 =
1¯
1¯
Ë 2
Ë 2
AP =
2
2
(30 − 0) + (30 − 0) =
30 2 + 30 2 =
900 + 900 =
1800 ≈ 42.4 ft
Feedback
A
B
C
D
Correct!
Check your calculations and rounding.
Set up the yard on a coordinate plane so that the apple tree A is at the origin. Then use
the distance formula to find the distance.
Set up the yard on a coordinate plane so that the apple tree A is at the origin. Then use
the distance formula to find the distance.
PTS:
OBJ:
LOC:
KEY:
1
DIF: Average
1-6.5 Application
MTH.C.11.05.04.008
coordinate geometry | distance
REF:
STA:
TOP:
DOK:
3
19599fb2-4683-11df-9c7d-001185f0d2ea
NY.NYLES.MTH.05.GEO.G.G.67
1-6 Midpoint and Distance in the Coordinate Plane
DOK 1