Question

the equation of the median of the triangle with vertices (4,3),(-2,3),(1,-2) passing through (-1,-3) is​

Answer 1

5x-9y-22=0

Step-by-step explanation:

Step 1 of 3

See the attached figure

We have P (4,3), Q (-2,3), R (1,-2)

First we need to find out the midpoint "S" of the line QR

Mid-point = [(x1+x2)/2, (y1+y2)/2]

Mid-point = (1-2/2, -2+3/2)

Mid-point =S= (-1/2, 1/2)

Step 2 of 3

Now to find slope of the line PS = y2-y2/x2-x1

P (4, 3)

Slope of PS = 3-1/2/4+1/2

Slope =5/2/9/2

Slope of PS = 5/9

Step 3 of 3

Now equation of the line passing through the point (-1,-3) is given by

y-y1=m(x-x1)

y-(-3)=5/9(x-(-1)

y+3=5/9(x+1)

9(y+3)=5(x+1)

9y+27=5x+5

5x-9y-22=0

#SPJ2

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Given the equation of the median of the triangle with vertices (4,3),(-2,3),(1,-2) passing through (-1,-3) is

• So we have P(4,3) Q(-2,3) R(1,2)
• The midpoint of Q and R is S
• So we have (x1 + x2 / 2, y1 + y2 / 2)
• So we have the median S = (-2 + 1 / 2, -2 + 3 / 2)
•  Or S = (-1/2 , ½ )
• We get Slope of PS = m = y2 – y1 / x2 – x2
•          (-1/2,1/2 ) (4,3)
• Slope = 3 – ½ / 4 + ½
•          = 5/2 / 9/2
•           = 5/9
• The line passing through the point and the equation will be  (y – y1) = m(x – x1)
•            So the point is (-1,-3) and m = 5/9
•            So we get
•              Substituting we get  (y + 3) = 5/9 (x + 3)
•                          Y + 3 = 5x + 15 / 9
•              Simplifying we get  5x + 15 = 9y + 27
•                           5x – 9y – 12 = 0

Reference link will be

https://brainly.in/question/15834527