Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

# math problem?

Let C(x,y) be a point between A(1,6) and B(−9,26) that is four times as far from A as it is from B. Find C(x,y)

Relevance
• 4 weeks ago

C = (1A+4B)/5 = ((1,6)+4(−9,26))/5 = (-35,110)/5 = (-7,22)

Source(s): The point that partitions the line segment A to B into a ratio of a:b is (bA+aB)/(a+b).
• Philip
Lv 6
4 weeks ago

In going from A(1,6) to B(-9,26) the following

occurs: x falls 2 units 5 times.

.............y rises 4 units 5 times.

In order that C be 4 times as far from A that it is

from B, x falls 4 times and y rises 4 times, ie.,

x falls 8 units and y rises 16 units. Then, at C,

x = (1-8) = -7 and y = 6+16 = 22. So we have

C(-7,22).

• Pope
Lv 7
4 weeks ago

Point C divides AB internally in ratio 4:1. This works like a weighted mean. Since B is the nearer point, it gets the greater weight, 4, while A gets weight 1.

A(1, 6), B(-9, 26), C(x, y)

x = [1(1) + 4(-9)] / (4 + 1) = -7

y = [1(6) + 4(26)] / (4 + 1) = 22

C(-7, 22)

• 4 weeks ago

Imagine a line between A and B.  Divide that line into 5 parts.  5 because the segment between AC is 4 times as long as the segment between BC, so 4:1 =>> 4 + 1 = 5

Now find the change in x and the change in y for each segment

change in x per segment: (-9 - 1) / 5 = -10/5 = -2

change in y per segment: (26 - 6) / 5 = 20/5 = 4

Add 4 segments to each coordinate

(1 + 4 * (-2) , 6 + 4 * 4) =>

(1 - 8 , 6 + 16) =>

(-7 , 22)

The point is (-7 , 22)