1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
koban [17]
3 years ago
9

Given points A (-3,-4) and B (2,0), points P (-1,-12/5) partitions line AB in the ratio

Mathematics
1 answer:
kvv77 [185]3 years ago
7 0
\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&A&(~ -3 &,& -4~) 
&P&(~ -1 &,& -\frac{12}{5}~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AP=\sqrt{[-1-(-3)]^2+[-\frac{12}{5}-(-4)]^2}
\\\\\\
AP=\sqrt{(-1+3)^2+(-\frac{12}{5}+4)^2}\implies AP=\sqrt{2^2+\left( \frac{8}{5} \right)^2}
\\\\\\
AP=\sqrt{4+\frac{64}{25}}\implies AP=\sqrt{\cfrac{164}{25}}\implies AP=\cfrac{\sqrt{164}}{\sqrt{25}}
\\\\\\
\boxed{AP=\cfrac{2\sqrt{41}}{5}}



\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&P&(~ -1 &,& -\frac{12}{5}~) 
&B&(~ 2 &,& 0~)
\end{array}
\\\\\\
PB=\sqrt{[2-(-1)]^2+[0-\left(-\frac{12}{5}  \right)]^2}
\\\\\\
PB=\sqrt{(2+1)^2+\left( \frac{12}{5} \right)^2}\implies PB=\sqrt{9+\frac{144}{25}}\implies PB=\sqrt{\cfrac{369}{25}}
\\\\\\
PB=\cfrac{\sqrt{369}}{\sqrt{25}}\implies \boxed{PB=\cfrac{3\sqrt{41}}{5}}

so, let's check the ratio of AP:PB

\bf AP:PB\implies \cfrac{AP}{PB}\implies \cfrac{\frac{2\sqrt{41}}{5}}{\frac{3\sqrt{41}}{5}}\implies \cfrac{2\underline{\sqrt{41}}}{\underline{5}}\cdot \cfrac{\underline{5}}{3\underline{\sqrt{41}}}\implies \cfrac{2}{3}
You might be interested in
What is the measure of c?<br> A. 20<br> B. 14<br> C. 16<br> D. 22
Harman [31]

Answer:

A

Step-by-step explanation:

The measurements of the segments fall on similar triangles. This means the lengths of each segment can be found using proportions.

Remember, a proportion is an equation which sets equal ratios equal to each other.

\frac{c}{k}=\frac{a}{j}\\\\\frac{c}{32}= \frac{15}{24}

To solve for c, multiply numerators and denominators across the equal sign:

24c = 32(15)

24c = 480

c = 20

5 0
2 years ago
Solve the inequality. 3x + 7 &gt; 4x + 2
Svetlanka [38]

Answer:

answer is b

Step-by-step explanation:

explanation in the pic!

6 0
3 years ago
Big trouble what is 99-30
katovenus [111]
I think it is 69 the rat
6 0
2 years ago
What is the 1st term when −5z2 + 7z4 + 11z − 8z3 is arranged in descending order
patriot [66]
Descending order...largest to smallest
the largest one is the one with the biggest exponent
so the first term is : 7z^4
3 0
3 years ago
Read 2 more answers
Drag tiles to describe each fraction Tiles may be used once, more than once, or not at all.​
jonny [76]

Answer:

1/3 is less than 2/3

7/9 is greater than 2/3

4/10 is less than 2/3

4/6 is equal to 2/3

5 0
3 years ago
Other questions:
  • The floor of a canyon has an elevation of −14.5−14.5 feet. Erosion causes the elevation to change by −1.5−1.5 feet per year. How
    9·1 answer
  • Solve the equation .<br><br> The solution of the equation is <br> .
    13·2 answers
  • Graham uses a 10 by 10 grid to model a decreasing pattern. He cuts off a section representing a percent of the current area so t
    9·2 answers
  • Choose the two numbers from the box to complete
    8·1 answer
  • Whats the area and perimeter
    6·2 answers
  • that one kilogram of rice weigh the same as 10 bags containing 100 grams of beans each do you agree with her why or why not
    9·1 answer
  • Find the probability. There are six nickels and seven dimes in your pocket. You randomly pick a coin out of your pocket and then
    12·1 answer
  • PLEASE HELPPPPPPPPPPPPPPOOP
    9·2 answers
  • I have to find the area of the shaded region in the figure above and answer using an exact and approximate answer
    10·1 answer
  • Rewrite the following expression using the properties of loy
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!