Final answer:
The distance from Nina's house to her school is 7 units. The total distance from Nina's house to the school to the grocery store is equal to the total distance from Nina's house to the school to the community center.
Step-by-step explanation:
To calculate the distance from Nina's house to her school, we can use the formula for the distance between two points in the coordinate plane. The formula is
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of the house (-4, 10) and the school (-4, 3), we substitute the values into the formula:
distance = √((-4 - (-4))^2 + (3 - 10)^2)
distance = √(0^2 + (-7)^2)
distance = √(0 + 49)
distance = √49
distance = 7 units
Therefore, the distance from Nina's house to her school is 7 units.
To determine whether the total distance from Nina's house to the school to the grocery store is greater than the total distance from Nina's house to the school to the community center, we need to calculate each distance. The distance from the house to the school is 7 units. The distance from the school to the grocery store is 9 units (using the coordinates provided). The distance from the school to the community center is also 9 units (using the coordinates provided). Therefore, the total distance from Nina's house to the school to the grocery store is 7 + 9 = 16 units, and the total distance from Nina's house to the school to the community center is 7 + 9 = 16 units as well. So the two total distances are equal.