Question

a rectangle has vertices at $(-1,6)$, $(-1,-2)$, $(3,6)$, and $(3,-2)$. sara says the area of the rectangle is 16 square units and her work is shown.
saras work
step 1: base: $|-1|+|3| = 4$
step 2: height: $|6|+|-2| = 4$
step 3: area: $4\times4 = 16$ square units
where, if at all, did sara first make a mistake in finding the area of the rectangle?
no mistake
step 1
step 3
step 2

Explanation:

Step1: Calculate the base length

For points \((-1,6)\) and \((3,6)\) (or \((-1, - 2)\) and \((3,-2)\)), the base length is \(|3-(-1)|=|3 + 1|=4\). Sara's step 1 is correct.

Step2: Calculate the height length

For points \((-1,6)\) and \((-1,-2)\) (or \((3,6)\) and \((3,-2)\)), the height length is \(|6-(-2)|=|6 + 2|=8\), not \(|6|+|-2| = 6+2=8\) (Sara's calculation \(|6|+|-2|=4\) is wrong). The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) with \(x_1=x_2\) is \(|y_1 - y_2|\).

Answer:

Step 2