For the line segment whose end points are A (0,0) and B (4,3) , find the x coordinate for the point located 2/3 the distance from A to B

The coordinates of x are (1.6, 1.2).

Solution:

Given points of the line segment are A(0, 0) and B(4, 3)

X be the point divided the line segment AB in the distance .

i.e., in the ratio of 2 : 3.

Section formula:

Here, and m = 2, n = 3

Substitute these in the section formula,

X(x, y) = (1.6, 1.2)            

The coordinates of x are (1.6, 1.2).

(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