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?​

9 Use Structure Point K is of the way from 45 to L0 7 a What are the coordinates of Kif n 4 b What is a formula for the coordinates of K for any n class=

Respuesta :

Dividing the segments, it is found that:

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

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  • The endpoints are [tex]J(4,-5)[/tex] and [tex]L(0,-7)[/tex].
  • Point K is (x,y).
  • Since point K is [tex]\mathbf{\frac{1}{n}}[/tex] of the way from J to L, it means that:

[tex]K - J = \frac{1}{n}(J - L)[/tex]

And this is the answer to option b.

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Option a:

If [tex]\mathbf{n = 4}[/tex], it has that:

[tex]K - J = \frac{1}{4}(J - L)[/tex]

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:

[tex]K - J = \frac{1}{4}(J - L)[/tex]

[tex]x - 4 = \frac{1}{4}(4 - 0)[/tex]

[tex]x - 4 = 1[/tex]

[tex]x = 5[/tex]

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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:

[tex]K - J = \frac{1}{4}(J - L)[/tex]

[tex]y - (-5) = \frac{1}{4}(-5 - (-7))[/tex]

[tex]y + 5 = \frac{2}{4}[/tex]

[tex]y = \frac{1}{2} - 5[/tex]

[tex]y = \frac{1}{2} - \frac{10}[2}[/tex]

[tex]y = -\frac{9}{2}[/tex]

The coordinates of K if n = 4 are [tex](5,-frac{9}{2})[/tex]

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

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