Question

Find the distance between the points (-4, 5) and (2, -3).

Hint:

The order of subtraction doesn't matter because the difference is squared, making the result always non-negative.

Answer 1

Step 1: Understanding the Concept:
The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane is calculated using the distance formula derived from the Pythagoras theorem.
Step 2: Formula and Substitution:
Distance $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Given: $x_1 = -4, y_1 = 5$ and $x_2 = 2, y_2 = -3$.
\[ d = \sqrt{(2 - (-4))^2 + (-3 - 5)^2} \]
Step 3: Calculation:
\[ d = \sqrt{(2 + 4)^2 + (-8)^2} \] \[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ units} \]
Step 4: Final Answer:
The distance between the points is 10 units.