A, B, C are collinear, and B is between A and C. The ratio of AB to AC is 1/3 . If A at (7, - 1) and B is at (2, 1) what are the coordinates of point C?

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Ответ:

Hailey1313131313

10.12.2022

Mathematics

$\large\boxed{(x-4)^2+(y+3)^2=25}$

Step-by-step explanation:

The equation of a circle:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have the center (4, -3) and the point on the circle (9, -3).

The length of radius is equal to the distance between a center and an any point on a circle.

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Susbtitute:

$r=\sqrt{(9-4)^2+(-3-(-3))^2}=\sqrt{5^2+0^2}=\sqrt{5^2}=5$

The center (4, -3) → h = 4, k = -3.

Finally we have:

$(x-4)^2+(y-(-3))^2=5^2\\\\(x-4)^2+(y+3)^2=25$

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