Question

students are trying to find the distance between the two points (9,19) and (-2,15). find the mistake in each students work.
find the mistake for student 3.
distance = \\( \sqrt { ( 9 - ( - 2 ) ) ^ { 2 } + ( 19 - 15 ) ^ { 2 } } \\)
= \\( \sqrt { ( 11 ) ^ { 2 } + ( 4 ) ^ { 2 } } \\)
= 11 + 4
= 15
choose the correct answer below.
a. the student forgot the square root.
b. the student did not do the operations in the correct order. the student needed to square and add before taking the square root.
c. the student added 2 instead of - 2 for the x - coordinates.
d. the student subtracted 2 instead of - 2 for the x - coordinates.
show how to correctly find the distance between the two given points. substitute (9,19) for \\( ( x _ { 1 }, y _ { 1 } ) \\) and ( - 2,15 ) for \\( ( x _ { 2 }, y _ { 2 } ) \\) in the distance formula.
distance = \\( \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } \\)
= \\( \sqrt { ( - 2 - \square ) ^ { 2 } + ( 15 - \square ) ^ { 2 } } \\)

Explanation:

Step1: Analyze the student's error

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). The student calculated \(\sqrt{(11)^2+(4)^2}\) as \(11 + 4\). According to the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), we should first calculate the values inside the square - root (square the terms and then add them) before taking the square root. The student did addition before taking the square root.

Step2: Correctly apply the distance formula

Given \((x_1,y_1)=(9,19)\) and \((x_2,y_2)=(-2,15)\)

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Answer:

B. The student did not do the operations in the correct order. The student needed to square and add before taking the square root.