If Paul drops the groceries he purchased halfway between the grocery store and his home, where would that location be on the graph?
A. (0, -3/2)
B. (0, 3/2)
C. (6, -3/2)
D. (-12, 3/2)
Unfortunately, without additional information such as the coordinates of the grocery store and Paul's home, it is not possible to determine the exact location of where Paul dropped the groceries.
To determine where the location would be on the graph, we need to understand the given information. The question states that Paul drops the groceries halfway between the grocery store and his home.
Let's assume Paul starts at the grocery store, represented by the origin (0,0) on the graph, and his home is located at some point on the positive x-axis.
Since Paul drops the groceries halfway between the grocery store and his home, the point would be equidistant from the grocery store and his home.
Let's say the distance from the grocery store to the home is x units. That means the distance from the grocery store to the midpoint (i.e., the location where the groceries are dropped) is x/2 units.
Since the grocery store is at the origin (0,0), and the groceries are dropped halfway, the midpoint would have a y-coordinate of 0. This rules out options A and C because they have non-zero y-coordinates.
Now, we need to determine the x-coordinate of the midpoint. Since the groceries are dropped halfway, the x-coordinate of the midpoint would be x/2.
From the given options, only option B has a y-coordinate of 3/2 and an x-coordinate of 0, which matches our calculations. Therefore, the location where Paul drops the groceries would be represented by (0, 3/2) on the graph.
Therefore, the correct answer is B. (0, 3/2).
To determine the location where Paul dropped the groceries, we need to understand the given information and use it to locate the point on the graph.
Let's break down the information provided:
- The grocery store is one endpoint.
- Paul's home is the other endpoint.
- Paul dropped the groceries halfway between the grocery store and his home.
Based on this, we can assume that the grocery store is at the point (0, 0) on the graph since no coordinates are given for it. Now, let's calculate the coordinates for the location where Paul dropped the groceries.
First, we need to determine the distance between the grocery store and Paul's home. Since the groceries were dropped halfway, this distance must be equal from the grocery store to the dropped groceries and from the dropped groceries to Paul's home.
Now, let's assume that Paul's home is located at point (x, y) on the graph. The distance from the grocery store to Paul's home can be calculated using the distance formula:
Distance = sqrt((x - 0)^2 + (y - 0)^2)
Since the groceries were dropped halfway, the distance from the grocery store to the location where Paul dropped the groceries is half of the distance from the grocery store to Paul's home:
Distance = sqrt((x/2 - 0)^2 + ((y/2) - 0)^2)
Since this distance is equal to the distance from the dropped groceries to Paul's home, we can set up an equation:
sqrt((x - 0)^2 + (y - 0)^2) = sqrt((x/2 - 0)^2 + ((y/2) - 0)^2)
Simplifying this equation, we get:
x^2 + y^2 = (x^2)/4 + (y^2)/4
Now, let's solve this equation to find the value of x and y. Bringing all the terms to one side, we get:
3x^2/4 = 3y^2/4
Simplifying this equation, we have:
x^2 = y^2
From this equation, we can see that x = y or x = -y.
However, since we know that Paul's home is the endpoint, we can assume that the coordinates (x, y) are positive. Therefore, x = y.
This means that the point where Paul dropped the groceries is on the line y = x or y = -x.
Looking at the answer choices, the only point on the graph that lies on the line y = x or y = -x is option B: (0, 3/2).
So, the correct answer is B. (0, 3/2).