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lorasvet [3.4K]

3 years ago

9

The rectangle is 3 3⁄4 centimeters long and 2 1⁄2 centimeters wide. What is the area of this rectangle?

1 answer:

scZoUnD [109]3 years ago

6 0

Answer:

The answer to your question is Area = 9 3/8

Step-by-step explanation:

Data

length = 3 3/4 cm

width = 2 1/2 cm

Process

1.- Write the equation of the Area of a rectangle

Area = length x width

2.- Convert the values to improper fractions

3 3/4 = (12 + 3)/ 4 = 15/4

2 1/2 = (4 + 1) / 2 = 5/2

3.- Substitution

Area = (15/4)(5/2)

4.- Simplification

Area = 75/8

5.- Convert to a mixed fraction

9

8 75

3

6.- Result

Area = 9 3/8

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8) Find the endpoint Cif M is the midpoint of segment CD and M (2, 4) and D (5,7)

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9. a. (-6, -1)

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Step-by-step Explanation:

8. Given the midpoint M(2, 4), and one endpoint D(5, 7) of segment CD, the coordinate pair of the other endpoint C, can be calculated as follows:

let $D(5, 7) = (x_2, y_2)$

$C(?, ?) = (x_1, y_1)$

$M(2, 4) = (\frac{x_1 + 5}{2}, \frac{y_1 + 7}{2})$

Rewrite the equation to find the coordinates of C

$2 = \frac{x_1 + 5}{2}$ and $4 = \frac{y_1 + 7}{2}$

Solve for each:

$2 = \frac{x_1 + 5}{2}$

$2*2 = \frac{x_1 + 5}{2}*2$

$4 = x_1 + 5$

$4 - 5 = x_1 + 5 - 5$

$-1 = x_1$

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$4*2 = \frac{y_1 + 7}{2}*2$

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Coordinates of endpoint C is (-1, 1)

9. a.Given segment AB, with midpoint M(-4, -5), and endpoint A(-2, -9), find endpoint B as follows:

let $A(-2, -9) = (x_2, y_2)$

$B(?, ?) = (x_1, y_1)$

$M(-4, -5) = (\frac{x_1 + (-2)}{2}, \frac{y_1 + (-9)}{2})$

$-4 = \frac{x_1 - 2}{2}$ and $-5 = \frac{y_1 - 9}{2}$

Solve for each:

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$-4*2 = \frac{x_1 - 2}{2}*2$

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$-8 + 2 = x_1 - 2 + 2$

$-6 = x_1$

$x_1 = -6$

$-5 = \frac{y_1 - 9}{2}$

$-5*2 = \frac{y_1 - 9}{2}*2$

$-10 = y_1 - 9$

$-10 + 9 = y_1 - 9 + 9$

$-1 = y_1$

$y_1 = -1$

Coordinates of endpoint B is (-6, -1)

b. The midpoint of a segment, is the middle of the segment. It divides the segment into two equal parts. The answer is TRUE.

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