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Lubov Fominskaja [6]
3 years ago
8

The point (3 , k) is a distance of 5 units from (0 , 1). Find the two possible values of k.

Mathematics
1 answer:
valkas [14]3 years ago
7 0
D =√(x2-x1)^2 + (y2-y1)^2
......._____________
5 =√(3-0)^2 + (k-1)^2
.......__________
5 =√3^2 + (k-1)^2

25 = 9 + (k-1)^2

16 = k^2 - 2k + 1

k^2 -2k - 15 = 0

(k - 5)(k + 3) = 0

k - 5 = 0.....or.......(k + 3) = 0

k = 5.........or.......k = -3
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Answer:

Side 1 = 8, side 2=6, side 3=3 1/3 or 10/3

Step-by-step explanation:

We can set up a proportion comparing the sides of the original triangle to the new triangle.

The original triangle has sides 12, 9, and 5. The new triangle has sides 8, e, and f (use whatever letters you like, it doesn't matter, but for me, e is the side with the middle length and f is the side with the shortest length.

We can write 3 ratios, with the length of the new triangle over the length of the old triangle.

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To figure out e and f, put each ratio equal to 8/12.

<u>8  </u> =  <u>e</u>  Then multiply both sides of the equation by 9 and get <u>72 </u> = e, 6=e.

12     9                                                                                              12

<u>8  </u> =  <u>f </u> Then multiply both sides of the equation by 9 and get <u>40 </u> = f, <u>10</u>=f.

12     5                                                                                              12          3

10/3 can be rewritten as 3 1/3.

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