Answer: Approximately 6.4 units
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Explanation:
The origin is the point (0,0)
Use the distance formula to find the distance from (0, 0) to (4, -5)
Let
[tex](x_1,y_1) = (0,0)\\\\(x_2,y_2) = (4,-5)\\\\[/tex]
be our two points. Plug those values into the distance formula below and use a calculator to compute
[tex]d = \sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\\\\d = \sqrt{\left(0-4\right)^2+\left(0-(-5)\right)^2}\\\\d = \sqrt{\left(0-4\right)^2+\left(0+5\right)^2}\\\\d = \sqrt{\left(-4\right)^2+\left(5\right)^2}\\\\d = \sqrt{16+25}\\\\d = \sqrt{41} \ \text{ exact distance}\\\\d \approx 6.40312 \ \text{ approximate distance}\\\\d \approx 6.4\\\\[/tex]
The distance between the two points (0,0) and (4,-5) is approximately 6.4 units.
