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3 years ago

Find the midpoint of the line segment whose endpoints are (-2, 5) and (6, -9). (4, -4) (2, -2) (1, -4)

Mathematics

1 answer:

Rus_ich [418]3 years ago

8 0

Answer:

(2,-2)

Step-by-step explanation:

The midpoint of the line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ has coordinates

$\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

If the endpoints of the line segment are (-2,5) and (6,-9), then the midpoint has the coordinates

$\left(\dfrac{-2+6}{2},\dfrac{5+(-9)}{2}\right)\\ \\\left(\dfrac{4}{2},\dfrac{-4}{2}\right)\\ \\(2,-2)$

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Answer:

Step-by-step explanation:

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3 years ago

the combined age of april and laura is 23 years. laura's age is two years more than half of april's age. what is laura's age

Kipish [7]

Laura's age is 9 years.

Solution:

Let x be the age of April.

Laura's age = 2 years more than half of April's age

<u>Convert statement into algebraic expression:</u>

Half of April's age = $\frac{x}{2}$

2 years more than half of April's age = $\frac{x}{2}+2$

Combined age of April and Laura = 23

⇒ April's age + Laura's age = 23

$$\Rightarrow \ \ x+(\frac{x}{2}+2) =23$

$$\Rightarrow \ \ x+\frac{x}{2}+2 =23$

$$\Rightarrow \ \ \frac{x}{1}+\frac{x}{2}+\frac{2}{1} =23$

To add the fractions make the denominators same.

Multiplying 2 on both numerator and denominator of unlike terms, we get

$$\Rightarrow \ \ \frac{x\times2}{1\times2}+\frac{x}{2}+\frac{2\times2}{1\times2} =23$

$$\Rightarrow \ \ \frac{2x}{2}+\frac{x}{2}+\frac{4}{2} =23$

Denominators are same, now add the fractions.

$$\Rightarrow \ \ \frac{2x+x+4}{2} =23$

Do cross multiplication.

$$\Rightarrow \ \ 2x+x+4=23\times2$

$$\Rightarrow \ \ 3x=46-4$

$$\Rightarrow \ \ 3x=42$

$$\Rightarrow \ \ x=14$

Aprils's age = 14 years

Laura's age = $\frac{14}{2}+2$

= 7 + 2

Laura's age = 9

Hence Laura's age is 9 years.

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3 years ago

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Sedaia [141]

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3 years ago

Allen is 20 years older than his cousin Jim. in 3 years, Allen will be twice as old as Jim. how old are allan and jim now

lesya [120]

Answer:

First of all this question makes no complate sense if this was in real life. But the answer is: Allen is 23 years old and Jim woukd be 12 1/2 years old.

Step-by-step explanation:

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