Question

Can someone please help me with this geometry homework?

Answer 1

The distances between the two points, in units, are given as follows:

7. $\sqrt{2}$

8. $2\sqrt{17}$

9. $3\sqrt{2}$

10. $3\sqrt{5}$

The midpoints are given as follows:

11. (7,-4.5).

12. (2,4).

13. (7,0.5).

14. (5.5,-1.5).

What is the distance between two points?

Suppose that we have two points, $(x_1,y_1)$ and $(x_2,y_2)$. The distance between them is given by:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

For item 7, the points are (-3,-2) and (-4,-3), hence the distance is:

$D = \sqrt{(-4 + 3)^2 + (-3 + 2)^2} = \sqrt{2}$

For item 8, the points are (-3,1) and (5,3), hence the distance is:

$D = \sqrt{(5 + 3)^2 + (3 - 1)^2} = \sqrt{68} = 2\sqrt{17}$

For item 9, the points are (-3,0) and (0,-3), hence the distance is:

$D = \sqrt{(0 + 3)^2 + (-3 - 0)^2} = \sqrt{18} = 3\sqrt{2}$

For item 10, the points are (1,-2) and (4,4), hence the distance is:

$D = \sqrt{(4 - 1)^2 + (4 + 2)^2} = \sqrt{45} = 3\sqrt{5}$

What is the midpoint concept?

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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