Triangle PQR has vertices P(0,12) Q(7,11) ans R(-2,2) Find the eaquation of the triangles median through point Q
if you sketch this you will see that the median from Q, bisects segment PR
to write the equation of the median you need to find the midpoint of PR
P(0,12), R(-2,2)
using the midpoint formula
1/2 (x1 + x2), 1/2 (y1 + y2)
1/2(0 + -2), 1/2(12 + 2)
1/2(-2), 1/2(14)
Midpoint (-1,7)
you want the equation through (-1,7) and (7,11)
y - y1 = (y2 - y1)/(x2 - x1) (x - x1)
y - 7 = (11 - 7)/(7 + 1) (x + 1)
y - 7 = 4/8 (x + 1)
y - 7 = 1/2 (x + 1)
y - 7 = 1/2 x + 1/2
y = 1/2x + 15/2
check my math,
Again...cheater, cheater, pumpkin eater!
To find the equation of the median through point Q, we first need to find the midpoint of the side PR. The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) can be found using the formulas:
Midpoint x-coordinate = (x₁ + x₂) / 2
Midpoint y-coordinate = (y₁ + y₂) / 2
In this case, the coordinates of points P and R are P(0,12) and R(-2,2) respectively. Let's find the midpoint of PR.
Midpoint x-coordinate = (0 + (-2)) / 2 = -1
Midpoint y-coordinate = (12 + 2) / 2 = 7
So, the midpoint of PR is (-1, 7).
Next, we can find the equation of the line passing through points Q and the midpoint of PR. The equation of a straight line can be found using the point-slope form:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line, and m is the slope.
We already have the coordinates of the midpoint (-1, 7) as (x₁, y₁), and we know that point Q(7, 11) also lies on the line. So, let's calculate the slope.
Slope (m) = (y₂ - y₁) / (x₂ - x₁)
= (11 - 7) / (7 - (-1))
= 4 / 8
= 1/2
Now, substitute the values into the equation:
y - 7 = (1/2)(x - (-1))
Simplifying,
y - 7 = (1/2)(x + 1)
2(y - 7) = x + 1
2y - 14 = x + 1
2y = x + 15
Therefore, the equation of the triangle's median through point Q is 2y = x + 15.