Question

a rectangle has vertices at $(-3,2),(7,2),(7,-5)$, and $(-3,-5)$. jordan says the area of the rectangle is 70 square units.
jordans work
step 1: base: $|-3|+|7|=10$
step 2: height: $|-5|+|2|=7$
step 3: area: $10\times7 = 70$ square units
which is true of jordans solution?
jordan is not correct because he did not add correctly before multiplying the dimensions.
jordan correctly found the area of the rectangle by adding the base and the height.
jordan correctly found the area of the rectangle by multiplying the base and the height.
jordan is not correct because he did not find the absolute value before multiplying the dimensions.

Explanation:

Step1: Calculate the base length

For the base, since the \(y -\)coordinates of \((-3,2)\) and \((7,2)\) are the same. The length of the base is \(|7-(-3)|=|7 + 3|=10\). Jordan's calculation of the base \(|-3|+|7|=10\) is correct as \(|-3|+|7|=3 + 7=10\).

Step2: Calculate the height length

For the height, since the \(x -\)coordinates of \((7,2)\) and \((7,-5)\) are the same. The length of the height is \(|2-(-5)|=|2 + 5|=7\). Jordan's calculation of the height \(|-5|+|2|=5 + 2=7\) is correct.

Step3: Calculate the area of the rectangle

The area formula of a rectangle is \(A=\text{base}\times\text{height}\). Substituting the base \(b = 10\) and height \(h=7\) into the formula, we get \(A=10\times7 = 70\) square units.

Answer:

Jordan correctly found the area of the rectangle by multiplying the base and the height.