Answer:
(0,5)
Step-by-step explanation:
Since the ratio is 1/3 and the difference between the two is 6 and 3, x would be 0 and y would be 5.
The coordinates of the point [tex]B[/tex] on the line [tex]AC[/tex], such that [tex]AB:AC = 1:3[/tex] are [tex](-5 \frac{5}{4})[/tex].
The coordinates of a point [tex](x,y)[/tex] that divides a line externally with end point points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] in a ratio [tex]m:n[/tex] are:
[tex]x=\frac{m x_2 - n x_1}{m-n}[/tex] and [tex]y=\frac{m y_2 - n y_1}{m-n}[/tex]
This is also known as section formula.
Here, [tex]A(-2,4)[/tex] and [tex]C(4,7)[/tex].
A point [tex]B[/tex] is on the line [tex]AC[/tex] such that [tex]AB:AC=1:3[/tex].
So, [tex]x_1=-2, y_1=4, x_2=4, y_2=7, m=1[/tex] and [tex]n=3[/tex].
Coordinates of [tex]B[/tex] are:
[tex]x=\frac{m x_2 - n x_1}{m-n}[/tex] and [tex]y=\frac{m y_2 - n y_1}{m-n}[/tex]
[tex]x=\frac{1 \times 4 - 3 \times -2}{1-3}[/tex] and [tex]y=\frac{1 \times 7 - 3 \times 4}{1-3}[/tex]
[tex]x=\frac{4 + 6}{-2}[/tex] and [tex]y=\frac{7 - 12}{-2}[/tex]
[tex]x=\frac{10}{-2}[/tex] and [tex]y=\frac{-5}{-2}[/tex]
[tex]x=-5[/tex] and [tex]y=\frac{5}{2}[/tex].
So, coordinates of [tex]B[/tex] are [tex](-5, \frac{5}{2})[/tex].
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