Chapter 1: Orienting Yourself: The Use of Coordinates

Exercise

Question

Question: 4

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Plot point Z (5, -6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides.

(Comment: Answers may differ from person to person.)

Answer

1
Construct a right-angled triangle with Z (5, -6) as the right-angle . Choose convenient lengths for the two perpendicular sides.
Coordinate graph showing point Z (5, -6) and a right-angled triangle IZN with perpendicular sides of 3 units and 4 units.
Right-angled triangle IZN constructed with point Z (5, -6) as the right-angle vertex.
Draw a horizontal line segment 4 units long to the left of Z and a vertical line segment 3 units long above Z.
Hence, NZ = 4 units and IZ = 3 units.
2
Find the length of IN using the theorem.
\text{IN = $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 units$ $\quad$ ${color:#625b5f}[perpendicular sides are IZ = 3 units and NZ = 4 units.]{/color}$}
3
Write the lengths of all three sides of triangle IZN.
Answer: For the construction shown, IZ = 3 units, NZ = 4 units, and IN = 5 units.
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