ANALYTICAL GEOMETRY TEST
BANK DIFFERENTIAL CALCULUS
(TECHNOLOGICAL INSTITUTE OF THE
PHILIPPINES)
, ANALYTICAL GEOMETRY TEST BANK
Member:
Desiderio, Caren
Ebora, Patricia Mae
Gaganao, Pearl Angelie
I. DISTANCE BETWEEN TWO POINTS
1. Lieutenant Santos orders an air strike in the battlefield targeting the enemy at a
coordinate (2, 5). If he is positioned at a coordinate (-14, -12), how far is he from the
target area? If the danger zone is within the 10 km radius from the strike point, is Lt.
Santos safe? (Let 1 unit = 1 km)
Choices:
A. 23.5
B. 26.5
C. 24.5
D. 22.5
35
Answer: A
Given:
𝑥1 =-14
𝑥2 = 2
𝑦1 =-12
Solution:
Distance Formula
𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
𝑑 = √(2 − (−14))2 + (5 − (12))2
𝑑 = √(2 − (−14))2 + (5 − (12))2
𝑑 = √(2 + 14))2 + (5 + 12))2
𝑑 = √(16))2 + (17))2
𝑑 = √(16))2 + (17))2
𝑑 = √256 + 289
𝑑 = √545
𝒅 = 𝟐𝟑. 𝟑𝟓
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,2. Chester and his father stood on their newly bought rectangular lot whose length and
width are 6 and 4 meters, respectively. His father told him that the place they are standing
at is one of the four boundary points of their lot which is 2, 5 meters away. What is the
distance of Chester and his father
Choices:
A. 2.6
B. 2.7
C. 2.8
D. 2.9
Answer: A
Given:
𝑥1=6
𝑥2=2
𝑦1=2
𝑦25
Solution:
Distance Formula
𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
𝑑 = √(2 − 6)2 + (5 − 2)2
𝑑 = √−42 + (3))2
𝑑 = √(−16 + 9
𝑑 = √7
𝒅 =2.6
3. Jerry and jean decide to run at the same time starting 5:30 am with jerry going northwest
and Jean going northeast until they meet halfway to their destination. Jerry runs at a rate
of 5 miles per hour traveling from point A to point R and then to point C. Jean runs
directly from point A to point C at the rate of 3 miles per hour. Which of them reaches
their destination first?
Choices:
A. 1.8
B. 1.6
C. 1.4
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, D. 1.5
Answer: C
Given:
Jerry’s rate=5 miles per hour
Jean’s rate= 3 miles per hour
Solution:
Jerry’s rate = 5 miles per hour
𝑑 = 2𝑚𝑖 + 4 𝑚𝑖 + 1 𝑚𝑖 = 7𝑚𝑖
7𝑚𝑖
𝑡 = = 1.4 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟
5𝑚𝑖
It takes Jerry to run 1.4 miles per hour to reach their destination.
𝐽𝑒𝑎𝑛’𝑠 𝑟𝑎𝑡𝑒 = 3 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟
𝑑 = √6 − 2)2 + ( 7 − 4)2 = √16 + 9 = √25 = 5 miles
Time:
𝑑
𝑡 = = 1.6 ℎ𝑜𝑢𝑟𝑠
𝑟
Thus, Jerry gets from point A to C for 1.4 miles per hour that Jean who took 1.6
miles per hour.
4. On a map, Julie’s house is located at (−2, 5) and Jimmy’s house is at (6,−2). How long is
the direct path from Julie’s house to Jimmy’s house?
Choices:
A. 8.92
B. 8.93
C. 8.95
D. 8.94
Answer: D
Given:
𝑥1 = -2 𝑥2 = 6
Downloaded by Collins Mwaniki ()
BANK DIFFERENTIAL CALCULUS
(TECHNOLOGICAL INSTITUTE OF THE
PHILIPPINES)
, ANALYTICAL GEOMETRY TEST BANK
Member:
Desiderio, Caren
Ebora, Patricia Mae
Gaganao, Pearl Angelie
I. DISTANCE BETWEEN TWO POINTS
1. Lieutenant Santos orders an air strike in the battlefield targeting the enemy at a
coordinate (2, 5). If he is positioned at a coordinate (-14, -12), how far is he from the
target area? If the danger zone is within the 10 km radius from the strike point, is Lt.
Santos safe? (Let 1 unit = 1 km)
Choices:
A. 23.5
B. 26.5
C. 24.5
D. 22.5
35
Answer: A
Given:
𝑥1 =-14
𝑥2 = 2
𝑦1 =-12
Solution:
Distance Formula
𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
𝑑 = √(2 − (−14))2 + (5 − (12))2
𝑑 = √(2 − (−14))2 + (5 − (12))2
𝑑 = √(2 + 14))2 + (5 + 12))2
𝑑 = √(16))2 + (17))2
𝑑 = √(16))2 + (17))2
𝑑 = √256 + 289
𝑑 = √545
𝒅 = 𝟐𝟑. 𝟑𝟓
Downloaded by Collins Mwaniki ()
,2. Chester and his father stood on their newly bought rectangular lot whose length and
width are 6 and 4 meters, respectively. His father told him that the place they are standing
at is one of the four boundary points of their lot which is 2, 5 meters away. What is the
distance of Chester and his father
Choices:
A. 2.6
B. 2.7
C. 2.8
D. 2.9
Answer: A
Given:
𝑥1=6
𝑥2=2
𝑦1=2
𝑦25
Solution:
Distance Formula
𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
𝑑 = √(2 − 6)2 + (5 − 2)2
𝑑 = √−42 + (3))2
𝑑 = √(−16 + 9
𝑑 = √7
𝒅 =2.6
3. Jerry and jean decide to run at the same time starting 5:30 am with jerry going northwest
and Jean going northeast until they meet halfway to their destination. Jerry runs at a rate
of 5 miles per hour traveling from point A to point R and then to point C. Jean runs
directly from point A to point C at the rate of 3 miles per hour. Which of them reaches
their destination first?
Choices:
A. 1.8
B. 1.6
C. 1.4
Downloaded by Collins Mwaniki ()
, D. 1.5
Answer: C
Given:
Jerry’s rate=5 miles per hour
Jean’s rate= 3 miles per hour
Solution:
Jerry’s rate = 5 miles per hour
𝑑 = 2𝑚𝑖 + 4 𝑚𝑖 + 1 𝑚𝑖 = 7𝑚𝑖
7𝑚𝑖
𝑡 = = 1.4 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟
5𝑚𝑖
It takes Jerry to run 1.4 miles per hour to reach their destination.
𝐽𝑒𝑎𝑛’𝑠 𝑟𝑎𝑡𝑒 = 3 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟
𝑑 = √6 − 2)2 + ( 7 − 4)2 = √16 + 9 = √25 = 5 miles
Time:
𝑑
𝑡 = = 1.6 ℎ𝑜𝑢𝑟𝑠
𝑟
Thus, Jerry gets from point A to C for 1.4 miles per hour that Jean who took 1.6
miles per hour.
4. On a map, Julie’s house is located at (−2, 5) and Jimmy’s house is at (6,−2). How long is
the direct path from Julie’s house to Jimmy’s house?
Choices:
A. 8.92
B. 8.93
C. 8.95
D. 8.94
Answer: D
Given:
𝑥1 = -2 𝑥2 = 6
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