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MakcuM [25]
3 years ago
14

Triangle PQR has vertices P(4,-1),Q(-2,7), and R(9,9). Find an equation of the median and altitude from R.

Mathematics
2 answers:
Reil [10]3 years ago
5 0
If we are drawing altitude from R the PQ will be base of this triangle. So we can say Median from R will cut on Midpoint of PQ. So firstly we will find mid point of PQ Which is S given as below:
P(4,-1) , Q (-2,7)

Let Co-ordinate of S is (x,y)
So x =  \frac{x_1+x_2}{2}
x =  \frac{4-2}{2} =  \frac{2}{2} = 1

y =  \frac{y_1+y_2}{2}
y =  \frac{-1+7}{2} =  \frac{6}{2}= 3
So midpoint of PQ is S(1,3).

Now we can find equation of RS
Co-ordinate of R is (9,9) and and S is (1,3).

In general equation of line from two point (x_1 , y_1) and (x_2,y_2) is
(y-y_1) =  \frac{y_2-y_1}{x__2-x_1}(x-x_1)

So equation of RS is

(y-9) =  \frac{9-3}{9-1} (x-1)
(y-9) =  \frac{6}{8}(x-1)
8(y-9) = 6(x-1)
8y-72 = 6x - 6
-72+6 = 6x - 8y
-66 = 6x-8y

So the equation of median is 6x - 8y = -66

sleet_krkn [62]3 years ago
5 0
Both of the equation of the median and altitude from R are the same: y=(3/4)x + 9/4, this means that they are at equal length so the triangle PQR is an isosceles (a triangle that has two sides of the same length).
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