Question

find the distance between the points (-5,1) and (3,-5)
distance =
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Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify the coordinates

Let \( (x_1, y_1) = (-5, 1) \) and \( (x_2, y_2) = (3, -5) \).

Step3: Substitute into the formula

First, calculate \( x_2 - x_1 = 3 - (-5) = 3 + 5 = 8 \) and \( y_2 - y_1 = -5 - 1 = -6 \).
Then, substitute these into the formula: \( d = \sqrt{(8)^2 + (-6)^2} \).

Step4: Simplify the expression

Calculate the squares: \( 8^2 = 64 \) and \( (-6)^2 = 36 \).
Add them: \( 64 + 36 = 100 \).
Take the square root: \( \sqrt{100} = 10 \).

Answer:

10