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Ahat [919]
2 years ago
10

Point C has the coordinates (-1,4) and point D has the coordinates (2,0). What is the distance between points C and D? Is ____ u

nits

Mathematics
1 answer:
beks73 [17]2 years ago
3 0

Answer: 5 units

Step-by-step explanation:

Distance = \sqrt{(x_{2 }- x_{1 })^2 + (y_{2 }- y_{1 })^2\\

= \sqrt{(2_ }- (-1)_{ })^2 + (0_{ }- 4_{ })^2

= \sqrt{(2_{ }+ 1_{ })^2 + (-4)^2_

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

= \sqrt{9+16}

= \sqrt{25}

= 5 units

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Irina18 [472]

Answer:

17. 6

18. 18 (as shown)

19. 10/3 = 3 1/3

20. 20/3 = 6 2/3

Step-by-step explanation:

17. For this, you can subtract the given length GB=12 from the length you found for problem 18, BF=18. Doing that tells you FG = 18-12 = 6, as you have marked on the diagram.

19. As with median BF, the point G divides it into two parts that have the ratio 1:2. The distance from G to D is the shorter of the distances, so you have ...

... GD = (1/3) CD = (1/3)·10 = 10/3

... GD = 3 1/3

20. You can subtract GD from CD to get CG, or you can multiply CD by 2/3. The result is the same either way.

... CG = CD -GD = 10 -3 1/3

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_____

<em>Comment on centroid and median</em>

The centroid (G) divides each median into parts in the ratio 1:2. Hence the shorter of those parts is half the length of the longer one, or 1/3 the total length of the median.

The longer of the parts is double the length of the shorter one, or 2/3 the total length of the median.

Your marking of median BF seems to show an understanding of these relationships. (Total length: 18; length of parts: 6 and 12.)

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Graph Transformations

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