Question 1

Find the length of a line segment ---

CD with endpoint C at (-3, 1) ad endpoint D at (5, 6). round your answer to the nearest tenth, if necessary.
A. 9.4
B. 5.4
C. 3.6 ]
D. 11.7

Find the midpoint of a segment FG with point F at (-6, 4) and midpoint G at (8, -2)
A. (-7, 3)
B. (7, -3)
C. (1, 1)
D. (-1, -1)

Find the slope of a line that passes through (-2, -3) and (1, 1)
A. 1/1
B. 1
C. 2
D. 4/3

Question 2

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &C&(~ -3 &,& 1~) % (c,d) &D&(~ 5 &,& 6~) \end{array}~ % distance value d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ CD=√([5-(-3)]^2+[6-1]^2)\implies CD=√((5+3)^2+(6-1)^2) \\\\\\ CD=√(8^2+5^2)\implies CD=√(64+25)\implies CD=√(89)$

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &F&(~ -6 &,& 4~) % (c,d) &G&(~ 8 &,& -2~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{8-6}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \left( \cfrac{2}{2}~~,~~\cfrac{2}{2} \right)\implies (1,1)$

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -2 &,& -3~) % (c,d) &&(~ 1 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{1-(-2)}\implies \cfrac{1+3}{1+2}\implies \cfrac{4}{3}$

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