Question

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is -99. Which equation can be used to find m, the midpoint of the two numbers?

Answer 1

Answer:

$m = \dfrac{a^2-99}{2a}$

Step-by-step explanation:

on a number line, m is the point that is the midpoint of two other points.

the distance between each of the points to the midpoint is 10 units..

if a is the point 10 units less than m

and b is the point 10 units greater than m,

then,

$m = a+10$

$m = b-10$

we can add the two equations to form the midpoint formula.

$2m = a+b$

we also know that the product of both numbers equal -99.

$ab = -99$

we can substitute either 'a' or 'b' to the equation of m.

$2m = a-\dfrac{99}{a}$

$m = \dfrac{a^2-99}{2a}$

and this is the equation for the midpoint of the two numbers.