Question

For the next five questions use triangle RST to do the problems below.
1. Write and equation of the line that contains the median of triangle of RST from S to line RT.

2. Write the equation of the line that contains the altitude of triangle RST from T to line RS.

3. What type of triangle is RST?

4. If a translation is done on triangle RST such that point S is move to coordinates of R, then the new coordinates for point R will be what?

5. If triangle RST is reflecte through the x-axis, which of the following will be the new coordinates for point T?

Answer 1

@terrenium

Answer 2

a)
First, find the median and formula to find the median is:
[(x1+x2+x3)/3, (y1+y2+y3)/3]; (where x1, x2 ,x3 are x-coordinates of points R,S,T and y1, y2 and y3 are y-coordinates of R,S,T). Say, M is the median point with coordinates (w,q).
Now , you have S(-4,7) and M(w,q).
find slope= (q-7)/(w+4). Now, use equation:
y-y1 = slope(x-x1)
y-7 = slope (x+4)
Solve and you will get the answer to a.

Answer 3

I need to write an equation. Not solve.

Answer 4

Just simply find the points of median and then you can write an equation. I have told you the solution, so its pretty straight forward to write the equation. If still not clear, ask.

Answer 5

So I got x + 2y= 6

Answer 6

@terrenium is that right?

Answer 7

median point is (0,5).
slope is (7-5)/(-4-0) = -1/2.
y-7 = -1/2*(x+4)
2y-14 =-4-x
x+2y = 10
This is your requires equation

Answer 8

okay, can you help with the other Q's?

Answer 9

b)
First find the slope of line RS.
say it is m1. the slope of altitude from T to line RS would be (say m2) m2 = -1/m1.
now, you have point T(4,7) and slope m2.
use y-7= m2(x+4) to find the required equation.

Answer 10

Slope is -3/2

Answer 11

c) The triangle seems isosceles to me. (I have not solved it)
I can't write down the whole procedure but I am giving you the basic idea.
You got S(-4,7) , T(4,7), R(0,1).
To find angle between ST and RT. find slope of line ST (say m1) and slope of line RT (say m2.) Angle would be tan(theta) = (m2-m1)/(1+m1*m2). Remember order is important of m1 and m2. Repeat the procedure for other sides and you ll get angles pretty much equal to 60 degrees (Am not sure because its my gesture)

Answer 12

okay

Answer 13

your required slope is 2/3. [-1/(-3/2)]

Answer 14

Im very confused