Question

on a number line, the coordinates of a and b are -3 and b, respectively. if the coordinate of the midpoint m of ab is 5, what is the value of b?

Explanation:

Step1: Recall midpoint formula

The midpoint \( M \) of two points \( A(x_1) \) and \( B(x_2) \) on a number line is given by \( M=\frac{x_1 + x_2}{2} \). Here, \( x_1=-3 \), \( x_2 = b \), and \( M = 5 \).

Step2: Substitute values into formula

Substitute the known values into the midpoint formula: \( 5=\frac{-3 + b}{2} \).

Step3: Solve for \( b \)

Multiply both sides of the equation by 2: \( 5\times2=-3 + b \), which simplifies to \( 10=-3 + b \). Then add 3 to both sides: \( b=10 + 3 \).

Answer:

13