You live at point A and your friend lives at point D. You let your friend borrow your calculator but you need it for tomorrow! One corner is at (-3, 1), another is at (3, 4), the next is at (7, 2), and the last is at (1, 1). You need to meet in the middle of your two houses. Which point do you meet at? Answer Choices:
(0, 0)
(1, 1)
(1.5, 1.5)
(2, 1.5)
To find the midpoint between two points, we average the x-coordinates of the two points and average the y-coordinates of the two points.
The x-coordinate of point A is -3, and the x-coordinate of point D is 1.
(-3 + 1)/2 = -2/2 = -1
The y-coordinate of point A is 1, and the y-coordinate of point D is 1.
(1 + 1)/2 = 2/2 = 1
Therefore, the midpoint is (-1, 1).
None of the answer choices match (-1, 1), so the correct answer is not listed.
The midpoint of AB is (2,4). Point A is at (7,2), where is point B?
Responses
(-3,6)
(4,2)
(5,2)
(6,-3)
To find the location of point B, we can use the midpoint formula which states that the midpoint of a line segment between two points (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2).
Given that the midpoint of AB is (2, 4) and point A is at (7, 2), we can substitute these values into the midpoint formula:
(2, 4) = ((7 + x2)/2, (2 + y2)/2)
Now we can solve for x2 and y2:
2 = (7 + x2)/2
4 = (2 + y2)/2
Multiplying both sides of the first equation by 2 yields:
4 = 7 + x2
Subtracting 7 from both sides gives:
-3 = x2
Multiplying both sides of the second equation by 2 yields:
8 = 2 + y2
Subtracting 2 from both sides gives:
6 = y2
Therefore, point B is at (-3, 6).
The answer is: (-3, 6).
To find the point in the middle of two houses, we need to find the average of the x-coordinates and the average of the y-coordinates. Let's calculate:
The x-coordinates of the two houses are -3 and 1. The average of -3 and 1 is (-3 + 1) / 2 = -2 / 2 = -1.
The y-coordinates of the two houses are 1 and 1. The average of 1 and 1 is (1 + 1) / 2 = 2 / 2 = 1.
Therefore, the point where you and your friend would meet is (-1, 1). None of the given answer choices match this point, so the correct answer is not provided.
To determine the meeting point between two houses, you can find the average of the x-coordinates and the average of the y-coordinates of the two houses. This will give you the midpoint between the two points.
For example, if one house is located at point A (-3, 1) and the other house is located at point D (1, 1), you can find the midpoint as follows:
- Average of x-coordinates: (-3 + 1) / 2 = -2 / 2 = -1
- Average of y-coordinates: (1 + 1) / 2 = 2 / 2 = 1
Therefore, the meeting point is (-1, 1).
Let's apply the same process to the given set of points and find the meeting point:
1. Average of x-coordinates: (-3 + 3 + 7 + 1) / 4 = 8 / 4 = 2
2. Average of y-coordinates: (1 + 4 + 2 + 1) / 4 = 8 / 4 = 2
The meeting point is (2, 2).
However, none of the answer choices match the calculated meeting point. It seems the answer choices are not correct or are not provided accurately. Please verify the answer choices or provide additional information to determine the correct meeting point.