Question 1

Use point p(-1,7), Q(0,-5) and R(3, 8) to calculate the following

A. Measure of PR
B. Slope of PQ
C. Midpoint of QR

Question 2

A)

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) P&({{ -1}}\quad ,&{{ 7}})\quad % (c,d) R&({{ 3}}\quad ,&{{ 8}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=√([3-(-1)]^2+[8-7]^2)\implies d=√((3+1)^2+(8-7)^2)$

B)

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) P&({{ -1}}\quad ,&{{ 7}})\quad % (c,d) Q&({{ 0}}\quad ,&{{ -5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-5-7}{0-(-1)}\implies \cfrac{-5-7}{0+1}$

C)

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) Q&({{ 0}}\quad ,&{{ -5}})\quad % (c,d) R&({{ 3}}\quad ,&{{ 8}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{{{ 3}} + {{0}}}{2}\quad ,\quad \cfrac{{{ 8}} + {{ (-5)}}}{2} \right)\implies \left(\cfrac{{{ 3}} + {{0}}}{2}\quad ,\quad \cfrac{{{ 8}} - {{ 5}}}{2} \right)$

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