Question

1. $(12\frac{1}{2},3\frac{3}{4})$ and $(-4\frac{1}{2},3\frac{3}{4})$ $\vert 12\frac{1}{2}\vert+\vert -4\frac{1}{2}\vert$ $=12\frac{1}{2}+4\frac{1}{2}$ $=17$ units 15. $(7\frac{1}{2},-5\frac{3}{4})$ and $(7\frac{1}{2},-1\frac{1}{4})$

Explanation:

Step1: <Subtract the y - coordinates>

Since the x - coordinates of the two points \((7\frac{1}{2},-5\frac{3}{4})\) and \((7\frac{1}{2},-1\frac{1}{4})\) are the same (\(x = 7\frac{1}{2}\)), we use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1=x_2\), \(d=\vert y_2 - y_1\vert\).
Let \(y_1=-5\frac{3}{4}=-\frac{5\times4 + 3}{4}=-\frac{23}{4}\) and \(y_2=-1\frac{1}{4}=-\frac{1\times4+1}{4}=-\frac{5}{4}\).
Then \(d=\vert-\frac{5}{4}-(-\frac{23}{4})\vert=\vert-\frac{5}{4}+\frac{23}{4}\vert\).

Step2: <Simplify the expression>

\(\vert-\frac{5}{4}+\frac{23}{4}\vert=\vert\frac{- 5 + 23}{4}\vert=\vert\frac{18}{4}\vert\).
Simplify \(\frac{18}{4}=\frac{9}{2}=4\frac{1}{2}\).

Answer:

\(4\frac{1}{2}\) units.