Exercise 4 Page 152

The distance from

A

to

X Z

refers to the shortest distance between the point and the line. This is always the length of the segment that's perpendicular to

X Z

. Therefore, we should substitute points

A

and

Z

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Substitute $(4, - 1)$ & $(3, 3)$

A Y = (4 - 3)^{2} + (- 1 - 3)^{2}

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Simplify right-hand side

Subtract terms

A Y = 1^{2} + (- 4)^{2}

Calculate power

A Y = 1 + 16

Add terms

A Y = 17

Calculate root

A Y = 4.12310 \dots

Round to $1$ decimal place(s)

A Y \approx 4.1