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

Hence, the answers are

A) 10 units

B) M =(0,4)