The point A is at –2 and the point B is at 7. Marissa would like to divide this line segment in a 4:3 ratio, and she would like to use the formula x = (x2 – x1) + x1.What values should she substitute into the formula?
The right formula is: [x - x₁] = (4 / 7) [x₂ - x₁]
And the values to substitute are: x₂ = 7 x₁ = - 2
Explanation:
1) Use these variables:
x₂ = the x-coordinate of point B = 7 x₁ = the x-coordinate of point A = - 2 x = the x-coordinate of the point that divides the line segment AB in a 4:3 ratio.
2) State the lengths:
length x - x₁ = x - x₁ length x₂ - x₁ = x₂ - x₁
2) Set a proportion: [x - x₁] / [x₂ - x₁] = 4 / 7
⇒ [x - x₁] = (4 / 7) [x₂ - x₁]
⇒ x = (4/7) [x₂ - x₁] + x₁
The values to substitute are: x₂ = 7 x₁ = - 2 Which leads to: ⇒ x = (4/7) [7 - (-2)] + (-2) = (4/7)(9) - 2 = 36/7 - 2 = [36 - 14] / 7 = 22 / 7
