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The endpoints of FG are F(3.75,9) and G (2,-12).
If point E divides FG in the ratio 3:4, the coordinates of point E are what?
If point H divides FE in the ratio 2:3, the coordinates of point H are what?

The Endpoints Of FG Are F3759 And G 212 If Point E Divides FG In The Ratio 34 The Coordinates Of Point E Are What If Point H Divides FE In The Ratio 23 The Coor class=

Sagot :

Using proportions, it is found that:

  • The coordinates of point E are (3,0).
  • The coordinates of point H are (3.45, 5.4).

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Point E divides FG in the ratio 3:4, hence:

[tex]E - F = \frac{3}{7}(G - F)[/tex]

This is used to find both the x and y coordinates.

For the x-coordinate, we have that:

[tex]E - F = \frac{3}{7}(G - F)[/tex]

[tex]x - 3.75 = \frac{3}{7}(2 - 3.75)[/tex]

x - 3.75 = -0.75.

x = 3.

For the y-coordinate:

[tex]E - F = \frac{3}{7}(G - F)[/tex]

[tex]y - 9 = \frac{3}{7}(-12 - 9)[/tex]

y - 9 = -9

y = 0.

The coordinates of point E are (3,0).

Point H divides FE in the ratio 2:3, hence:

[tex]H - F = \frac{2}{5}(E - F)[/tex]

This is used to find both the x and y coordinates.

For the x-coordinate, we have that:

[tex]H - F = \frac{2}{5}(E - F)[/tex]

[tex]x - 3.75 = \frac{2}{5}(3 - 3.75)[/tex]

x - 3.75 = -0.3.

x = 3.45.

For the y-coordinate, we have that:

[tex]H - F = \frac{2}{5}(E - F)[/tex]

[tex]y - 9 = \frac{2}{5}(0 - 9)[/tex]

y - 9 = -3.6

y = 5.4.

The coordinates of point H are (3.45,5.4).

More can be learned about proportions at https://brainly.com/question/24372153

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