The following are two ordered pairs: (h, -1) and (5,1). Answer the following questions with respect to these ordered pairs

Question

i) Represent the distance between these two points (h will appear in your answer).

ii) Represent the abscissa of the midpoint between these two points (h will appear in your answer).

iii) The distance between these two points is equal to the abscissa of the midpoint between these two points. Write an equation that represents this fact.

iv) Show all steps needed in order to solve the equation in part iii for h. Give the exact reduced answer and simplify all radicals. 

v) Using the value(s) for h that you obtained in step iv, write the ordered pair(s) whose ordinate is -1. 

Answer 1

Just take it a little at a time.

i) the distance formula is d = sqrt[(y₂-y₁)² + (x₂-x₁)²] so just plug in the x's and y's. you should get d = sqrt(29-10h+h²)

ii) the midpoint formula for the x value (abscissa) is x = (x₁ + x₂)/2 so plug in the x values. You should get x = (h+5)/2

iii) set them equal: sqrt(29-10h+h²) = (h+5)/2 and solve for h by squaring both sides. You should get:

3h² - 50h + 91 = 0 solve using the quadratic formula to get h = (25 + 4sqrt(22))/3 (notice there are two answers)

iv) Plug in the h to get two possible ordered pairs (h, -1)