Question

describe and correct the error a student made in finding the midpoint of cd with c(-4,5) and d(-1,-4). choose the correct answer below. a. the student used incorrect coordinates when calculating the midpoint. b. the student did not divide the numerator and denominator by 2 when calculating the midpoint. c. the student did not add the x - and y - coordinates when calculating the midpoint. d. the student swapped the x - and y - values when calculating the midpoint.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). For points \(C(-4,5)\) and \(D(-1,-4)\), the \(x\) - coordinate of the mid - point is \(\frac{-4+( - 1)}{2}=\frac{-4 - 1}{2}=-\frac{5}{2}\) and the \(y\) - coordinate is \(\frac{5+( - 4)}{2}=\frac{5 - 4}{2}=\frac{1}{2}\).

Step2: Analyze the student's error

The student made a sign error in the calculation of the \(y\) - coordinate. The correct formula application for the \(y\) - coordinate should be \(\frac{y_1 + y_2}{2}\), and the student did not add the \(y\) - coordinates correctly. The student's work shows incorrect arithmetic in adding the \(y\) - values.

Answer:

C. The student did not add the x - and y - coordinates when calculating the mid - point.