Question

Points A, B, C, and D are collinear. D is the midpoint of AC and C is the midpoint of AB. Find AB if AD = 2x + 6 and CB = 3x + 24.

Answer 1

We have A, B, C and D collinear potins. Also, we know that point D in the midpoint of AC and C is the midpoint of AB, AD = 2x +6 and CB = 3x+24, so:

`\begin{gathered} AB=2\cdot CB\text{, because C is the midpoint of AB} \\ AB=2\cdot(3x+24)=6x+48 \\ AC=CB=2\cdot AD,\text{because D is the midpoint of AC} \\ 3x+24=2\cdot(2x+6)=4x+12 \\ 24-12=4x-3x \\ 12=x \\ \text{Now, we replace the value of x to find the value of AB:} \\ AB=6\cdot12+48=120 \end{gathered}`

AB = 120