Question

Heather's work to find the distance between two points, r(-3,-4) and s(5,7), is shown: r s = ( ( - 4 ) - ( - 3 ) ) 2 ( 7 - 5 ) 2 = ( - 1 ) 2 ( 2 ) 2 = 1 4 = 5. What error, if any, did Heather make?

1) She substituted incorrectly into the distance formula.
2) She subtracted the coordinates instead of adding them.
3) She made a sign error when simplifying inside the radical.
4) She made no errors.

Answer 1

Heather made an error in the application of the distance formula by incorrectly substituting the coordinates leading to the wrong calculation. The corrected version involves correctly squaring the differences of x-coordinates (5 - (-3)) and y-coordinates (7 - (-4)), and then taking the square root of the sum of these squares.

Step-by-step explanation:

Heather made an error in substituting the values into the distance formula. The correct method is to use the difference between the respective x-coordinates of the two points and the difference between the y-coordinates of the two points. This process follows the Pythagorean theorem to find the distance between the two points in a coordinate plane.

The corrected version of the formula is as follows:

RS = √((5 - (-3))² + (7 - (-4))²) = √((5 + 3)² + (7 + 4)²)

RS = √(8² + 11²) = √(64 + 121) = √185

The answer is A. She substituted incorrectly into the distance formula.

Complete Question:

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS=sqrt((((-4)-(-3))^2)+(7-5)^2)

=sqrt((-1)^2+(2)^2)

=sqrt(1+4)

=sqrt(5)

What error, if any, did Heather make?

A. She substituted incorrectly into the distance formula.

B. She subtracted the coordinates instead of adding them.

C. She made a sign error when simplifying inside the radical.

D. She made no errors.