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3 years ago

Which of the points given divide the line segment AB in the ratio 2:3?

Mathematics

1 answer:

alexira [117]3 years ago

4 0

Answer: The correct answer is Choice D, (5, 7).

First, we need to identify the slope from A to B.
It will be -5/-5. In other words, to go from A to B, we move down 5 spaces and left 5 spaces.

If we are going to divide the segment, we are not going to move all 5 spaces in each direction.

Since we are looking for a 2:3 ratio, we are only moving 2 out of the total of 5 spaces. It is 2 over 5, because 2 + 3 makes a total of 5.

Therefore, we only move down 2 and left 2 spaces from Point A. That will put us at the point (5, 7).

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What is the equation of the line that passes through the points (4/5,1/5) and (1/2,3/2)?

Setler [38]

Answer:

$y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})$ point-slope form

$13x+3y=11$ (standard form)

Let me know if you prefer another form.

Step-by-step explanation:

The slope of a line can be found using $\frac{y_2-y_1}{x_2-x_1}$ provided you are given two points on the line.

We are.

Now you can use that formula. But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.

(4/5 , 1/5)

-( 1/2 , 3/2)

-----------------

3/10 -13/10

2nd/1st = $\frac{\frac{-13}{10}}{\frac{3}{10}}=\frac{-13}{3}$ is our slope.

So the following is point-slope form for a linear equaiton:

$y-y_1=m(x-x_1) \text{ where } m \text{ is slope and } (x_1,y_1) \text{ is a point on the line }$

Plug in a point $(x_1,y_1)=(\frac{1}{2},\frac{3}{2}) \text{ and } m=\frac{-13}{3}$ .

This gives:

$y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})$

I'm going to distribute:

$y-\frac{3}{2}=\frac{-13}{3}x-\frac{-13}{6}$

Now I don't like these fractions so I'm going to multiply both sides by the least common multiply of 2,3, and 6 which is 6:

$6y-9=-26x+13$

Add 26x on both sides:

$26x+6y-9=13$

Add 9 on both sides:

$26x+6y=22$ This is actually standard form of a line.

It can be simplified though.

Divide both sides by 2:

$13x+3y=11$ (standard form)

7 0

3 years ago

Read 2 more answers

The balance of Bryce's accounts is $16. Jada's account is $15 overdrawn. What is the difference between their accounts balance

Mrac [35]

16 - -15 = 31 (negative - negative = positive)

hope this helps! :)

3 0

3 years ago

Solve for x.<br> x-8=-20

NeX [460]

Answer:

Step-by-step explanation:

To solve:

x - 8 = -20

Simply add +8 to both sides of the equation.

It becomes :

x - 8 +8 = -20 + 8

Note that, -8 + 8 will cancel out, and results to zero.

Therefore the equation becomes :

x = -20 + 8

x = -12.

Hope this helped!

8 0

3 years ago

37. Watering a lawn requires 623 gallons of water for

Strike441 [17]

Answer:

6.23 gallons per square foot

Step-by-step explanation:

623/1000 = 6.23

6 0

2 years ago

EASY POINTS EVALUATION

dedylja [7]

Answer:

$\frac{4}{9}$

Step-by-step explanation:

$( \frac{16 {}^{ \frac{1}{2} } }{81 { }^{ \frac{1}{2} } }) \\ ( \frac{ {4}^{2 \times \frac{1}{2} } }{9^{2 \times \frac{1}{2} } }) \\ ( \frac{4^{1} }{9 ^{1} } ) \\ \frac{4}{9}$

6 0

2 years ago

Read 2 more answers