Plot point $\mathrm{Z}(5, -6)$ on the Cartesian plane. Construct a right-angled triangle $\mathrm{IZN}$ and find the lengths of the three sides. (Comment: Answers may differ from person to person.)

Since, $Z$ lies in Quadrant IV.

From graph,

$$Z = (5, -6)$$

$$I = (5, 0) \text{ (directly above } Z)$$

$$N = (0, -6) \text{ (directly right of } Z)$$

Angle at $Z$ is between $IZ$ (vertical) and $ZN$ (horizontal), so it is $90^\circ$.

Side lengths:

$$IZ = |(0) - (-6)| = 6 \text{ units}$$

$$ZN = |5 - 0| = 5 \text{ units}$$

$$IN \text{ (hypotenuse)} = \sqrt{5^2 + 6^2}$$

$$= \sqrt{25 + 36} = \sqrt{61} \text{ units.}$$

### Concept Applied

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is

$$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \text{ obtained directly from the}$$

Baudhāyana–Pythagoras theorem.