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15 units

Step-by-step explanation:

The distance between two points can be found using the following formula:

[tex]d\sf=\sqrt{(x_2-x_1)+(y_2-y_1)}[/tex]

Given points:

(-7, 5) and (2, -7)

where:

- x₁ = -7
- x₂ = 2
- y₁ = 5
- y₂ = -7

Substitute these points into the formula and simplify:

[tex]\sf d=\sqrt{(2-(-7))^2+((-7)-5)^2} \ \textsf{[simplify the radicand]}\\\\ d=\sqrt{(2+7)^2+(-12)^2} \ \textsf{[simplify]}\\\\d=\sqrt{(9)^2+(-12)^2} \ \textsf{[evaluate the power]}\\\\d=\sqrt{81+144} \ \textsf{[add]}\\\\d=\sqrt{225}\ \textsf{[simplify]}\\\\d=15[/tex]

The distance between the two points is 15 units.

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