Question

It is recommended that you work this out on graph paper to help answer the questions. Maria 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.):Her house is at (−4, 9).Her school is at (−4, 3).The community center is at (1, 3).The grocery store is at (−4, −8).Part A: Use absolute values to calculate the distance in units from Maria's house to her school. Show your work. (4 points)Part B: Is the total distance from Maria's house to the school to the grocery store greater than the total distance from Maria's house to the school to the community center? Justify your answer. (6 points)

Answer 1

Solution

Step 1:

Given data:

Her house is at (−4, 9).

Her school is at (−4, 3).

The community center is at (1, 3).

The grocery store is at (−4, −8).

Part A

Her house is at (−4, 9).

Her school is at (−4, 3).

$\begin{gathered} Distance\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ =\sqrt{(-4-(-4))^2+(3\text{ - 9\rparen}^2} \\ \\ =\text{ }\sqrt{0^2\text{ +\lparen-6\rparen}^2} \\ \\ =\text{ }\sqrt{36} \\ =\text{ 6 units} \end{gathered}$

Maria's house to her school is 6 units

Part B

The total distance from Maria's house to the school to the grocery store

= 6 + 11

= 17

The total distance from Maria's house to the school to the community center

= 6 + 6

= 12

YES

The total distance from Maria's house to the school to the grocery store is greater than the total distance from Maria's house to the school to the community center