Maria plots the locations of 4 places on a coordinate grid as given below
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.
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.
Please show me how to figure this question out?
Part A:The absolute value will always be positive. It would be 8 from her house to school
Part B: No it is less than because it is (-4,9) and her school is (-4,3) so the grocery store is (-4,-8) so the community center would be greater than the total distance.
A. (-4,9), (-4,3).
d^2 = (4-4)^2 + (3-9)^2.
d^2 = (0)^2 + (-6)^2 = 0 + 36 = 36,
d = 6 = Distance from Maria's house to school.
B. (-4,3), (-4,-8).
d^2 = (4-4)^2 + (-8-3), (^2.
d^2 = (0)^2 + (-11)^2 = 121.
d = 11 = Distance from school to grocery store.
6+d = 6+11 = 17 = Distance from Maria's house to school to grocery store.
(-4,3), (1,3).
d^2 = (1+4)^2 + (3-3)^2 = 25,
d = 5 = Distance from school to community center.
6+d = 6+5 = 11 = Dist. from Maria's home to school to community center.
Part A: To calculate the distance between two points on a coordinate grid, you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, Maria's house is at (-4, 9) and her school is at (-4, 3).
Using the formula, we can calculate the distance between these two points:
Distance = √((-4 - (-4))^2 + (3 - 9)^2)
= √((0)^2 + (-6)^2)
= √(0 + 36)
= √36
= 6
Therefore, the distance from Maria's house to her school is 6 units.
Part B: To find the total distance from Maria's house to different locations, you need to calculate the distance from one location to another and sum them up.
Total distance from house to school to grocery store:
Distance from house to school = 6 units (as calculated in Part A)
Distance from school to grocery store = √((-4 - (-4))^2 + (3 - (-8))^2)
= √((0)^2 + (11)^2)
= √(0 + 121)
= √121
= 11
Total distance from house to school to grocery store = 6 + 11 = 17 units.
Total distance from house to school to community center:
Distance from house to school = 6 units (as calculated in Part A)
Distance from school to community center = √((1 - (-4))^2 + (3 - 3)^2)
= √((5)^2 + (0)^2)
= √(25 + 0)
= √25
= 5
Total distance from house to school to community center = 6 + 5 = 11 units.
Since 17 units is greater than 11 units, 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.