Question

It is recommended that you work this out on graph paper to help answer the questions. Sean plots the locations of 4 places on a coordinate grid as given below (It is recommended that you work this out on graph paper to help answer the questions.):

His house is at (−4, 5).
His school is at (−4, 3).
The community center is at (6, 3).
The grocery store is at (−4, −9).

Part A: Use absolute values to calculate the distance in units from Sean's house to his school. Show your work. (4 points)

Part B: Is the total distance from Sean's house to the school to the grocery store greater than the total distance from Sean's house to the school to the community center? Justify your answer.

Answer 1

Explanation:

since the house, the school and the grocery store all have the same x coordinate (-4), they are on the same vertical line of x = -4.

and that means their distances are simply the differences in their y coordinates.

the only one different in that regard is the community center, but it is on the same y coordinate as the school, so the distance to the school is only the difference in their x coordinates.

A

so, the distance from house to school is

|5 - 3| = |3 - 5| = 2

as it is the same distance in either direction.

B

the distance from house to school to grocery store is the distance from house to school plus the distance from school to grocery store :

2 + |3 - -9| = 2 + |-9 - 3| = 2 + 12 = 14

now we need to find the distance from home to school to community center.

that is 2 + the distance from school to community center.

as mentioned above, since the school and the community center have the same y coordinate, their distance is the difference in their x coordinates :

|-4 - 6| = |6 - -4| = 10

so, in total the way house to school to community center is 2 + 10 = 12.

and that is shorter than the way house to school to grocery store, which is 14.

so, yes, the distance house to school to grocery store (14) is greater than the distance house to school to community center (12).