Question

question 3
eric counted the slope between (1,2) and (5,-6) to get the midpoint. he counted down 8 and over 4. to get the midpoint, he cut those in half and counted down 4 and over 2 getting to the point (3,-2). did he do this correctly?
no, he should have counted down 4, over 4.
no, he should have counted up 4, over 8.
no, he did the initial slope right, but did the midpoint wrong.
yes, he did this correctly.

Explanation:

Step1: Calculate the change in \(x\) and \(y\)

The formula for the change in \(x\) (\(\Delta x\)) is \(x_2 - x_1\), and for the change in \(y\) (\(\Delta y\)) is \(y_2 - y_1\).
Given the points \((x_1,y_1)=(1,2)\) and \((x_2,y_2)=(5, - 6)\)
\(\Delta x=5 - 1=4\)
\(\Delta y=-6 - 2=-8\) (counting down 8)

Step2: Find the mid - point using the mid - point formula

The mid - point formula is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\)
\(\frac{x_1 + x_2}{2}=\frac{1 + 5}{2}=\frac{6}{2}=3\)
\(\frac{y_1 + y_2}{2}=\frac{2+( - 6)}{2}=\frac{-4}{2}=-2\)
Also, if we halve \(\Delta x = 4\) (get \(2\)) and halve \(\Delta y=-8\) (get \(-4\), which is counting down 4), starting from \((1,2)\): \(x = 1+2 = 3\), \(y=2+( - 4)=-2\) (the same as using the mid - point formula)

Answer:

Yes, he did this correctly.