Question

9. Use Structure Point K is of the way from |(4,-5) to L(0, -7). a. What are the coordinates of Kif n = 4? b. What is a formula for the coordinates of K for any n?​

Answer 1

Dividing the segments, it is found that:

• a) The coordinates of K if n = 4 are $(5,-frac{9}{2})$
• b) $K - J = \frac{1}{n}(J - L)$

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• The endpoints are $J(4,-5)$ and $L(0,-7)$.
• Point K is (x,y).

• Since point K is $\mathbf{\frac{1}{n}}$ of the way from J to L, it means that:

$K - J = \frac{1}{n}(J - L)$

And this is the answer to option b.

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Option a:

If $\mathbf{n = 4}$, it has that:

$K - J = \frac{1}{4}(J - L)$

This is applied to find both the x-coordinate and the y-coordinate of K.

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• The x-coordinate of K is x.
• The x-coordinate of J is 4.
• The x-coordinate of L is 0.

Thus:

$K - J = \frac{1}{4}(J - L)$

$x - 4 = \frac{1}{4}(4 - 0)$

$x - 4 = 1$

$x = 5$

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• The y-coordinate of K is y.
• The y-coordinate of J is -5.
• The y-coordinate of L is -7.

Thus:

$K - J = \frac{1}{4}(J - L)$

$y - (-5) = \frac{1}{4}(-5 - (-7))$

$y + 5 = \frac{2}{4}$

$y = \frac{1}{2} - 5$

$y = \frac{1}{2} - \frac{10}[2}$

$y = -\frac{9}{2}$

The coordinates of K if n = 4 are $(5,-frac{9}{2})$

A similar problem is given at https://brainly.com/question/20847604