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Points X and Z are on a number line, and point Y partitions XZ into two parts so that the ratio of the length of XY to the length of YZ is 5:7. The coordinate of X is 1.3, and the coordinate of Y is 3.8. What is the coordinate of Z?

Respuesta :

SaniShahbaz

Answer:

The coordinate of [tex]Z=7.3[/tex].

Step-by-step explanation:

To determine:

What is the coordinate of Z?

Fetching Information and Solution Steps:

  • Points X and Y are on a number line
  • point Y partitions [tex]XZ[/tex] into two parts so that the ratio of the length of XY to the length of [tex]YZ[/tex] is 5:7
  • The coordinate of X is 1.3
  • the coordinate of Y is 3.8

The distance [tex]XY[/tex] = [tex]3.8-1.3 = 2.5[/tex]

As

Y is [tex]\frac{5}{12}[/tex] of the way from [tex]X[/tex] to [tex]Z[/tex]

So,

[tex]YZ[/tex] is [tex]\frac{7}{5}[/tex] as big as [tex]XY[/tex]

Therefore,

[tex]Z = 3.8 + (\frac{7}{5} )(2.5)[/tex]

[tex]Z=3.8+\frac{17.5}{5}[/tex]

[tex]Z=7.3[/tex]

Therefore, the coordinate of [tex]Z=7.3[/tex].

Keywords: coordinate, point, length, ratio

Learn more about coordinate and point from brainly.com/question/12120670

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The coordinate of Z is (4.43, 11.57)

The coordinate of X is (1, 3)

The coordinate of Y is (3, 8)

Let the coordinate of z be (x₂, y₂)

The ratio of division is 5:7

m = 5, and n = 7

Let the coordinate of y be (a, b)

a = 3, b = 8

[tex]a=\frac{mx_1+nx_2}{m+n}\\\\3= \frac{5(1)+7x_2}{5+7}\\\\3(12)=5+7x_2\\\\7x_2=36-5\\\\7x_2=31\\\\x_2=4.43[/tex]

[tex]ab=\frac{my_1+ny_2}{m+n}\\\\8= \frac{5(3)+7y_2}{5+7}\\\\8(12)=15+7y_2\\\\7y_2=96-15\\\\7y_2=81\\\\y_2=11.57[/tex]

The coordinate of Z is (4.43, 11.57)

Learn more here: https://brainly.com/question/14488098