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Norma-Jean [14]
3 years ago
11

What is the slope of the line that contains the points (-4,3) and (6,-3)

Mathematics
1 answer:
Naddika [18.5K]3 years ago
6 0
\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ -4 &,& 3~) 
%  (c,d)
&&(~ 6 &,& -3~)
\end{array}
\\\\\\
% slope  = m
slope =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-3}{6-(-4)}\implies \cfrac{-3-3}{6+4}
\\\\\\
\cfrac{-6}{10}\implies -\cfrac{3}{5}
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TS = √[(3 - 8 )² + (- 4 - 1)²] = 5√2

NS = √[(- 4 - 3 )² + (- 3 + 4)²] = 5√2

NA = AT = TS = NS = 5√2

m_{NA} = (- 3 - 2) / (- 4 - 1) = 1 ........ <em>(1)</em>

m_{TS} = (- 4 - 1) / (3 - 8 ) = 1 ......... <em>(2)</em>

From (1) and (2) ⇒ NA║TS

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m_{NS} = ( - 4 + 3) / ( 3 + 4) = - 1 / 7 .... <em>(4)</em>

From (3) and (4) ⇒ AT║NS

Thus, NATS is rhombus.

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