Question

question 11 (multiple choice worth 2 points) (perimeter and area on the coordinate plane mc) the vertices of a rectangle are plotted on the coordinate grid shown. what is the area of the rectangle shown? 40 square units 45 square units 80 square units 90 square units

Explanation:

Step1: Find the length of the rectangle

The length is the distance between \((-5, 5)\) and \((4, 5)\). Since the y - coordinates are the same, we use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1 = y_2\): \(d=\vert x_2 - x_1\vert\). Here, \(x_1=-5\), \(x_2 = 4\), so length \(l=\vert4-(-5)\vert=\vert4 + 5\vert=9\).

Step2: Find the width of the rectangle

The width is the distance between \((-5, 5)\) and \((-5,-5)\). Since the x - coordinates are the same, we use the formula \(d=\vert y_2 - y_1\vert\). Here, \(y_1 = 5\), \(y_2=-5\), so width \(w=\vert-5 - 5\vert=\vert-10\vert = 10\).

Step3: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A=l\times w\). Substituting \(l = 9\) and \(w = 10\), we get \(A=9\times10 = 90\) square units. Wait, no, wait. Wait, let's re - check the points. Wait, \((-5,5)\) and \((4,5)\): the distance is \(4-(-5)=9\). \((-5,5)\) and \((-5,-5)\): the distance is \(5-(-5)=10\)? Wait, no, \(y\) - coordinate difference: \(5-(-5)=10\)? Wait, no, the vertical distance between \(y = 5\) and \(y=-5\) is \(5-(-5)=10\)? Wait, no, the absolute value of \(-5 - 5=-10\), absolute value is 10. Then area is length times width, \(9\times10 = 90\)? But wait, let's check the other points. \((4,5)\) and \((4,-5)\): the distance is \(5-(-5)=10\), and \((-5,-5)\) and \((4,-5)\): distance is \(4-(-5)=9\). So length is 9, width is 10, area is \(9\times10 = 90\)? Wait, but let's check the options. Wait, maybe I made a mistake. Wait, \((-5,5)\) and \((4,5)\): the x - values are - 5 and 4, so the difference is \(4-(-5)=9\). \((-5,5)\) and \((-5,-5)\): the y - values are 5 and - 5, difference is \(5-(-5)=10\). Then area is \(9\times10 = 90\). So the area is 90 square units.

Answer:

90 square units (corresponding to the option "90 square units")