Question 1208013
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The other tutor has discussed part (a).
I'll focus on part (b) only.


Use the slope formula to find the slope of line AB.
{{{matrix(1,17,"Given","points:","A=","(",x[1],",",y[1],") = ","(-2,0)","and","B=","(",x[2],",",y[2],") = ","(-4,4)")}}}


{{{m = slope = rise/run = matrix(1,3,"change","in","y")/matrix(1,3,"change","in","x")}}}


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (4 - 0)/(-4 - (-2))}}}


{{{m = (4 - 0)/(-4 + 2)}}}


{{{m = (4)/(-2)}}}


{{{m = -2}}}
Line AB has slope -2.


Follow a similar process to find:
line BC has slope 1/12
line AC has slope 1/2


Compare slopes AB and AC.
They are -2 and 1/2 in that exact order.
The slopes multiply to -1, so it proves lines AB and AC are perpendicular. 
They meet at a 90 degree angle.
This in turn proves triangle ABC is a right triangle (where the 90 degree angle is at point A).


See this page
<a href="https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1207909.html">https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1207909.html</a>
for a proof as to why slopes that multiply to -1 lead to perpendicular lines.
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