The distance between the two points is (2,-3)and (k,9) is 13 units find k

Mathematics

1 answer:

docker41 [41]3 years ago

8 0

Step-by-step explanation:

$\sqrt{(k - 2)^{2} + {(9 + 3)}^{2} } = 13 \\ \\ \therefore \: \sqrt{k^{2} - 2 \times 2k + 2^{2} + {(12)}^{2} } = 13 \\ \\ \therefore \: \sqrt{k^{2} - 4k + 4 + 144 } = 13\\ \\ \therefore \: \sqrt{k^{2} - 4k + 148 } = 13 \: \\ \: \: \: \: \: \: squaring \: both \: sides \\ \\ k^{2} - 4k + 148 = 169 \\ \\ \therefore \: k^{2} - 4k + 148 - 169 = 0\\ \\ \therefore \: k^{2} - 4k - 21 = 0\\ \\ \therefore \: k^{2} - 7k + 3k - 21 = 0\\ \\ \therefore \: k(k - 7) + 3(k - 7) = 0 \\ \\ \therefore \: (k - 7) (k+ 3) = 0 \\ \\ \therefore \: (k - 7) = 0 \: or \: (k+ 3) = 0 \\ \\ \therefore \: k = 7 \: or \: k = - 3 \\ \\ \huge \purple{ \boxed{\therefore \:k = \{ - 3, \: \: 7 \}}}$

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see attached

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Dilation is the transformation that changes the size of something. When you choose ×110% on a copy machine, you are making all the dimensions in the copy equal to 1.1 times the dimensions of the original, for example. That is dilation by a factor of 1.1, or 110%.

Here, you're asked to dilate triangle ABC by a factor of 3. That means all of the dimensions on the dilated figure will be 3 times their length on the original.

The center of dilation is point P. That means all the distances from point P are multiplied by 3.

In the attached figure, a gray arrow has been drawn from point P to each of the points A, B, and C. Then two more arrows of the same length are drawn in the same direction. The total distance at the end of the 3 arrows is 3 times the original distance from point P. These are the points A', B', and C' you are asked to draw. Connecting these points gives the dilated triangle A'B'C'.

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