Point C open parentheses 4 comma space 2 close parentheses divides the line segment joining points A open parentheses 2 comma space minus 1 close parentheses and B open parentheses x comma space y close parentheses such that A C : C B equal 3 : 1. What are the coordinates of point B?

Question:

Point C (4,2) divides the line segment joining points A(2,-1) and B(x, y) such that AC:  CB = 3:1.

What are the coordinates of point B?

Step-by-step explanation:

Given

Required

Find the coordinates of B

Coordinates of a line segment is calculated using:

In this case:

---

The equation becomes

So, the coordinates of B is:

Solving further

Multiply through by 4

By comparison:

So:

The coordinates of B is:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240