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julia-pushkina [17]
3 years ago
6

A rectangle has its vertices at (-4, -3), (-4,7), (1,7), (1, -3). What part, in percent, of the rectangle is located in Quadrant

III?

Mathematics
1 answer:
Rasek [7]3 years ago
3 0

Consider the attached figure. The whole rectangle is ABCD, while AEGF is the part located in the third quadrant. In fact, this quadrant is composed by all the points with both coordinates negative.

To answer the question, let's compute the area of the two rectangles and see what part of ABCD is AEGF.

A and B have the same x coordinate, so the length of AB is given by the absolute difference of their y coordinates:

\overline{AB} = |A_y-B_y| = |-3-7| = |-10| = 10

Similarly, but exchanging the role of x and y, we compute the length of BC:

\overline{BC} = |B_x-C_x| = |-4-1| = |-5| = 5

So, the area of the rectangle is \overline{AB} \cdot \overline{BC} = 10\cdot 5 = 50

The same procedure allows us to compute width and height of the sub-rectangle in the third quadrant:

\overline{AE} = |A_y-E_y| = |-3-0| = |-3| = 3

\overline{EG} = |E_x-G_x| = |-4-0| = |-4| = 4

So, the area of the portion located in the third quadrant is \overline{AE} \cdot \overline{EG} = 3\cdot 4 = 12

This means that the ratio between the two area is

\cfrac{\text{area }AEGF}{\text{area }ABCD} = \cfrac{12}{50}

If we want this ratio to be a percentage, just make sure that the denominator is 100:

\cfrac{12}{50} = \cfrac{12}{50}\cdot \cfrac{2}{2} = \cfrac{24}{100} = 24\%

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2 years ago
What is the location of the point (5, 0) translates 4 units to the down and reflected across the y-axis?
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STEP-BY-STEP EXPLANATION:

Given information

The given ordered point = (5, 0)

Step 1: We need to translate the point 4 units down

To translate down means we will be subtracting a value from the y--axis

Hence, we have

\begin{gathered} (x,\text{ y) }\rightarrow\text{ (x, y-b)} \\ \text{where b = 4} \\ (5,\text{ 0) }\rightarrow\text{ (5, 0 - 4)} \\ (5,\text{ 0) }\rightarrow\text{ (5, -4)} \end{gathered}

When translated 4 units down, we got (5, -4)

Step 2: Reflect over the y-axis

The general rule for reflecting over the y-axis is (-x, y)

This means the value of x will be negated and the value of y will remain the same

\begin{gathered} \text{Over the y-ax}is \\ (x,\text{ y) }\rightarrow\text{ (-x, y)} \\ (5,\text{ -4) }\rightarrow\text{ (-5, -4)} \end{gathered}

Step 3: the graph the point

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2 years ago
the larger of two positive numbers is 5 more then the smaller. The product of the numbers is 66. find the numbers
Serjik [45]

Answer: 30.5 and 35.5

Step-by-step explanation:

We can use a system of linear equations to find out the answer to this problem. The larger number will be x and the smaller number will be y.

x=y+5

x+y=66

Substitute y+5 in for the bottom equation to get y+5+y=66. Simplify to get 2y+5=66. Subtract 5 from both sides and get 2y=61. Divide by 2 to get y=30.5. This is the smaller number. Add 5 to get the bigger number, which is 35.5

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nignag [31]

Answer:

Step-by-step explanation:

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3 years ago
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