Answered

IDNLearn.com is committed to providing high-quality answers to your questions. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.

points a,b, and c make the triangle ABC and are at the coordinates A(-2,9), B(-33,13) and c(-21,25) point D is the midpoint of BC and AD is a median of ABC, the equation of the median can be given by ax+by=c where A B and C

what is most simple way to answer this

Sagot :

Semsee45idn

Answer:

[tex]2x+5y=41[/tex]

Step-by-step explanation:

Median of a triangle:  A line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Vertex:  The point where any two sides of a triangle meet.

Given vertices of a triangle:

  • A = (-2, 9)
  • B = (-33, 13)
  • C = (-21, 25)

Step 1

Find the midpoint of BC (Point D) by using the Midpoint formula.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

  • [tex]\text{Let }(x_1,y_1)=\sf B=(-33,13)[/tex]
  • [tex]\text{Let }(x_2,y_2)=\sf C=(-21,25)[/tex]

Substitute the defined endpoints into the formula:

[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]

Therefore, D = (-27, 19).

Step 2

Find the slope of the median (line AD) using the Slope formula.

Define the points:

  • [tex]\textsf{let}\:(x_1,y_1)=\sf A=(-2,9)[/tex]
  • [tex]\textsf{let}\:(x_2,y_2)=\sf D=(-27,19)[/tex]

Substitute the defined points into the Slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]

Therefore, the slope of the median is -²/₅.

Step 3

Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]

Simplify and rearrange the equation so it is in standard form Ax+By=C:

[tex]\implies 5(y-9)=-2(x+2)[/tex]

[tex]\implies 5y-45=-2x-4[/tex]

[tex]\implies 2x+5y-45=-4[/tex]

[tex]\implies 2x+5y=41[/tex]

Conclusion

Therefore, the equation of the median is:  

2x + 5y = 41

View image Semsee45
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.