Question

c is the midpoint of $overline{bd}$. if $bc = 4x$ and $cd = x + 6$, what is $bc$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since C is the mid - point of $\overline{BD}$, then $BC = CD$. So we set up the equation $4x=x + 6$.

Step2: Solve the equation for x

Subtract x from both sides: $4x−x=x + 6−x$, which simplifies to $3x=6$. Then divide both sides by 3: $\frac{3x}{3}=\frac{6}{3}$, so $x = 2$.

Step3: Find the value of BC

Substitute $x = 2$ into the expression for BC. Since $BC = 4x$, then $BC=4\times2=8$.

Answer:

8