Question

Write an equation of the line that contains the median of triangle RST from S to line RT. R(-2,-2) S(1,4) T(7,1)

Answer 1

the median from point S to line RT divides the line RT in half.
Can you find the mid point of (-2,-2) and (7,1)?

Answer 2

the midpoint i got was (5/2,-1/2)

Answer 3

do you know how to find the equation of a line given 2 points?
S (1,4) and mid pt (5/2, -1/2)

Answer 4

one way is find the slope: change in y divided by change in x
then use
one of the points to find b
in the equation
y= mx+b

Answer 5

i was thinking altitude, not median

Answer 6

i got y=-3x+7

Answer 7

now i need to show that the median of the triangle from S is also the altitude from S. how do i do that?

Answer 8

an altitude forms a right angle. that means the lines RT and the medians have slopes m and -1/m
so find the equation of the line through R and T, it's slope should be 1/3

Answer 9

or just find the slope between R and T. don't really need the entire equation

Answer 10

just to be clear: perpendicular lines have slopes m and -1/m

Answer 11

yeah the reciprocal but i already said what the slope between R and T. is (5/2,-1/2)

Answer 12

that is the mid point. the slope is different (for starters, slope is a number, not a pair)

Answer 13

the slope is 3/5?

Answer 14

R(-2,-2), T(7,1)
change in y divided by change in x
(1 - (-2))/(7 - (-2))= 3/9 = 1/3

Answer 15

You must know how to find the slope, because you found it for the median line.

Answer 16

oh i forgot it was a -2 so um now what do i do?

Answer 17

you write down: slope of the line RT is 1/3
slope of line from S to mid pt of RT is -3
-3*1/3 = -1
therefore they are perpendicular, and form a right angle. A line from a vertex to the opposite leg that forms a right angle is an altitude.

Answer 18

is that a negative sign before the first 3?

Answer 19

no it is a minus sign

(just kidding). It is -3, the slope of the median line.

Answer 20

um isn't -3 -3*1/3= -2?

Answer 21

you said
i got y=-3x+7, so its slope is -3

and we found the slope of R to T is 1/3
so the slopes are negative reciprocals -3 * 1/3 = -1
so the lines are perpendicular.
that means your median line is also an altitude.