(a) Ans: (5, 6)
Point A is clearly marked at the intersection of the x-coordinate 5 and y-coordinate 6.
(b) Ans: \(y=-\frac{4}{5}x+3\)
The line passes through (0,3) (y-intercept) and slope \(m = \frac{-1-3}{5-0} = -\frac{4}{5}\).
(c) Ans: \(y=-\frac{4}{5}x-2\)
Parallel lines have the same slope. Using point B (5,-6), substitute into \(y = -\frac{4}{5}x + c\) to find \(c = -2\).
(d)(i) Ans: \(y=\frac{5}{4}x+4\)
Perpendicular slope is \(\frac{5}{4}\) (negative reciprocal). Using point C (8,14), solve for \(c = 4\).
(d)(ii) Ans: 8.54 or 8.544…
Distance formula: \(\sqrt{(8-5)^2 + (14-6)^2} = \sqrt{9 + 64} = \sqrt{73} \approx 8.54\).
(d)(iii) Ans: (4, 6)
Midpoint of B (5,-6) and C (8,14): \(\left(\frac{5+8}{2}, \frac{-6+14}{2}\right) = (4, 6)\).
