Question

For the line segment whose endpoints are X(1, 2) and Y(6, 7), find the x value for the

Answer 1

Answer:

3) x ≈ 2.7  

Step-by-step explanation:

X is at (1,2) and Y is at (6,7)

A point that is ⅓ of the distance from X to Y also divides the differences of the x-and y-coordinates in the same ratio.

For the x-coordinate,

x₂ - x₁ = 7 - 2 = 5

⅓ × 5  = 5/3  

1 + 5/3 = 8/3

The x-coordinate of the point is x = 8/3 ≈ 2.7.

The graph below shows that the point one-third of the distance from X to Y has an x-coordinate of approximately 2.7.

Answer 2

Answer:

3) 2.7

Step-by-step explanation:

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be determined by:

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

Since the points are X(1, 2) and Y(6, 7). The distance between the two points is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(6-1)^2+(7-2)^2}=\sqrt{50}$

the x value for the  point located 1/3 the distance from X to Y,

$x=\frac{x_2-x_1}{3}=\frac{6-1}{3}=1.7$

The x value = $x_1+1.7 = 1+1.7 = 2.7$