Question

midterm review (optional)
score: 23.64/100 answered: 4/15
question 5
find the distance between the points (-3,-2) and (4,1)
distance =
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Explanation:

Step1: Identify the formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-3,y_1 = - 2,x_2=4,y_2=1\).

Step2: Substitute the values

Substitute the values into the formula: \((x_2 - x_1)=4-(-3)=4 + 3=7\) and \((y_2 - y_1)=1-(-2)=1 + 2=3\). Then \(d=\sqrt{(7)^2+(3)^2}\).

Step3: Calculate the squares

\(7^2 = 49\) and \(3^2=9\). So \(d=\sqrt{49 + 9}\).

Step4: Sum and find the square - root

\(49+9 = 58\), and \(d=\sqrt{58}\).

Answer:

\(\sqrt{58}\)