Given:
A line passes through the points (-1, -1) and (5,8).
To find:
Which points lie on the same line?
Solution:
If a line passes through two points, then the equation of the line is:
![y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:
![y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))](https://tex.z-dn.net/?f=y-%28-1%29%3D%5Cdfrac%7B8-%28-1%29%7D%7B5-%28-1%29%7D%28x-%28-1%29%29)
![y+1=\dfrac{8+1}{5+1}(x+1)](https://tex.z-dn.net/?f=y%2B1%3D%5Cdfrac%7B8%2B1%7D%7B5%2B1%7D%28x%2B1%29)
![y+1=\dfrac{9}{6}(x+1)](https://tex.z-dn.net/?f=y%2B1%3D%5Cdfrac%7B9%7D%7B6%7D%28x%2B1%29)
![y+1=\dfrac{3}{2}(x+1)](https://tex.z-dn.net/?f=y%2B1%3D%5Cdfrac%7B3%7D%7B2%7D%28x%2B1%29)
Multiply both sides by 2.
![2(y+1)=3(x+1)](https://tex.z-dn.net/?f=2%28y%2B1%29%3D3%28x%2B1%29)
![2y+2=3x+3](https://tex.z-dn.net/?f=2y%2B2%3D3x%2B3)
![2y=3x+3-2](https://tex.z-dn.net/?f=2y%3D3x%2B3-2)
![y=\dfrac{3}{2}x+\dfrac{1}{2}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B3%7D%7B2%7Dx%2B%5Cdfrac%7B1%7D%7B2%7D)
So, the equation of the line is
.
Now, check each point for this equation.
Putting
, we get
![y=\dfrac{3}{2}(-3)+\dfrac{1}{2}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B3%7D%7B2%7D%28-3%29%2B%5Cdfrac%7B1%7D%7B2%7D)
![y=\dfrac{-9+1}{2}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B-9%2B1%7D%7B2%7D)
![y=\dfrac{-8}{2}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B-8%7D%7B2%7D)
![y=-4](https://tex.z-dn.net/?f=y%3D-4)
Similarly,
For
.
For
.
For
.
For
.
For
.
Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.
The ratio of the sides will be constant. Then the value of the length of line segment SA will be 3 ft.
The missing diagram is given below.
<h3>What is the triangle?</h3>
A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangles ΔABC and ΔSBT are the similar triangles.
Then the ratio of the sides will be constant.
BS / SA = BT / TC
10 / SA = 9 / 2.7
SA = 3
Then the value of the length of line segment SA will be 3 ft.
More about the triangle link is given below.
brainly.com/question/25813512
#SPJ1
Answer:
$4,523.40
Step-by-step explanation:
The cell phone cost is $124.65 per month. With 12 months in a year, we multiply $124.65 x 12 to get the answer $1,507.80. Since one year equals $1,507.80, we multiply this answer by 3 for 3 years to get $4,523.40. Thus three years of service with $124.65 a month would equal $4,523.40.
Answer:
A. -205.7 kJ
Step-by-step explanation:
The overall enthalpy of reaction be calculated when the intermediate steps are present
formed in a multi-step process.
Answer:
49
Step-by-step explanation:
devaughn= x+15
sydney= x
set an equation adding both their ages
x+x+15=113
2x+15=113
subtract 15 from both sides
2x=98
x=49
sydney is 49