The distances between the two points, in units, are given as follows:
7. ![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
8. ![2\sqrt{17}](https://tex.z-dn.net/?f=2%5Csqrt%7B17%7D)
9. ![3\sqrt{2}](https://tex.z-dn.net/?f=3%5Csqrt%7B2%7D)
10. ![3\sqrt{5}](https://tex.z-dn.net/?f=3%5Csqrt%7B5%7D)
The midpoints are given as follows:
11. (7,-4.5).
12. (2,4).
13. (7,0.5).
14. (5.5,-1.5).
<h3>What is the distance between two points?</h3>
Suppose that we have two points,
and
. The distance between them is given by:
![D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
For item 7, the points are (-3,-2) and (-4,-3), hence the distance is:
![D = \sqrt{(-4 + 3)^2 + (-3 + 2)^2} = \sqrt{2}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%28-4%20%2B%203%29%5E2%20%2B%20%28-3%20%2B%202%29%5E2%7D%20%3D%20%5Csqrt%7B2%7D)
For item 8, the points are (-3,1) and (5,3), hence the distance is:
![D = \sqrt{(5 + 3)^2 + (3 - 1)^2} = \sqrt{68} = 2\sqrt{17}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%285%20%2B%203%29%5E2%20%2B%20%283%20-%201%29%5E2%7D%20%3D%20%5Csqrt%7B68%7D%20%3D%202%5Csqrt%7B17%7D)
For item 9, the points are (-3,0) and (0,-3), hence the distance is:
![D = \sqrt{(0 + 3)^2 + (-3 - 0)^2} = \sqrt{18} = 3\sqrt{2}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%280%20%2B%203%29%5E2%20%2B%20%28-3%20-%200%29%5E2%7D%20%3D%20%5Csqrt%7B18%7D%20%3D%203%5Csqrt%7B2%7D)
For item 10, the points are (1,-2) and (4,4), hence the distance is:
![D = \sqrt{(4 - 1)^2 + (4 + 2)^2} = \sqrt{45} = 3\sqrt{5}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B%284%20-%201%29%5E2%20%2B%20%284%20%2B%202%29%5E2%7D%20%3D%20%5Csqrt%7B45%7D%20%3D%203%5Csqrt%7B5%7D)
<h3>What is the midpoint concept?</h3>
The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
Hence, for item 11, the midpoint is given by:
[0.5(9 + 5), 0.5(1-10)] = (7,-4.5).
For item 12, the midpoint is given by:
[0.5(-5 + 9), 0.5(7 + 1)] = (2,4).
For item 13, the midpoint is given by:
[0.5(9 + 5), 0.5(9 - 8)] = (7,0.5).
For item 14, the midpoint is given by:
[0.5(10 + 1), 0.5(4 - 7)] = (5.5,-1.5).
More can be learned about the distance between two points at brainly.com/question/18345417
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