Question

a rectangle has vertices at $(-2,11)$, $(-2,4)$, $(6,11)$, and $(6,4)$. pablo says the area of the rectangle is 49 square units and his work is shown. pablos work step 1: base: $|-2|+|6| = 8$ step 2: height: $11 - 4 = 7$ step 3: area: $8\times7 = 49$ square units where, if at all, did pablo first make a mistake finding the area of the rectangle? step 1 no mistake step 3 step 2

Explanation:

Step1: Calculate the base length

The base length of a rectangle with vertices \((x_1,y)\) and \((x_2,y)\) is \(|x_2 - x_1|\). Here, for points \((-2,11)\) and \((6,11)\) (or \((-2,4)\) and \((6,4)\)), the base \(b=|6-(-2)|=|6 + 2|=8\). Pablo's step 1 is correct.

Step2: Calculate the height

The height of a rectangle with vertices \((x,y_1)\) and \((x,y_2)\) is \(|y_2 - y_1|\). For points \((-2,11)\) and \((-2,4)\) (or \((6,11)\) and \((6,4)\)), the height \(h = |11 - 4|=7\). Pablo's step 2 is correct.

Step3: Calculate the area

The area of a rectangle is \(A=\text{base}\times\text{height}\). Substituting \(b = 8\) and \(h=7\), we get \(A=8\times7=56\) square units. Pablo made a mistake in step 3 as \(8\times7
eq49\).

Answer:

Step 3