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Functions, 2ADV EQ-Bank 12

  1. Show the equation of \(AC\) is \(3 x+4 y-16=0\).   ( 2 marks)

  2. Show that \(BC\) is not perpendicular to \(AC\).   (2 marks)

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a.   \(\text{Proof (See Worked Solutions)}\)

b.   \(\text{Proof (See Worked Solutions)}\)

Show Worked Solution

a.    \(A(0,4), C(4,1)\)

\(m_{AC}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-4}{4-0}=-\dfrac{3}{4}\)

\(\text{Equation of line with} \ \ m=-\dfrac{3}{4} \ \ \text{through}\ (0,4):\)

\(y-y_1\) \(=m\left(x-x_1\right)\)
\(y-4\) \(=-\dfrac{3}{4}(x-0)\)
\(y-4\) \(=-\dfrac{3}{4} x\)
\(4 y-16\) \(=-3 x\)
\(3 x+4 y-16\) \(=0\)

 

b.    \(B(3,0), C(4,1)\)

\(m_{BC}=\dfrac{1-0}{4-3}=1\)

\(m_{AC} \times m_{BC}=-\dfrac{4}{3} \times 1=-\dfrac{4}{3} \neq-1\)

\(\therefore AC \ \text{is not} \ \perp \text{to} \ BC.\)