Question

What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary.
x = ____
y = ____Choose matching definition
a. (-3.5, 2.3)
b. (1.2, -4.7)
c. -2.6
5.2
d. (-4, -5)

Answer 1

The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 are (-2.6,5.2).

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.

If a point (x,y) divides the line segment joining the points A(x1,y1) and B (x2,y2) is in the ratio m:n, then

$x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n}$

Here,

m:n = 3:10

The endpoint of line AB are at: A(-4,8) and B(2,-4)

We substitute the given values to obtain:

x= 3*2+10*(-4)/3+10

x= -34/13

x= -2.6

and

y= 3*(-4)+10*(8)/3+10

y= 68/13

y= 5.2

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