Question

Line AB has endpoints A(4,7) and B(-4,1)A)Find the length of ABB)Find the coordinates of the midpoint of AB(If possible without the graph)

Answer 1

A) 10 units

B) M =(0,4)

A) Since line AB has those endpoints let's apply the distance formula so that we can find out the length AB:

$d_{AB}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

Now we can plug into that points A and B:

$\begin{gathered} d_{AB}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d_{AB}=\sqrt[]{(-4_{}-4_{})^2+(1_{}-7)^2} \\ d_{AB}=10 \end{gathered}$

B) To find out the midpoint we must use the following formula:

$\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ M=(\frac{4+(-4)}{2},\frac{7+1}{2}) \\ M=(0,4) \end{gathered}$

Hence, the answers are

A) 10 units

B) M =(0,4)