given triangle PQR with vertices P(0,-8), Q(4,-9) and R(-2,-3), find the length of the midsegment connecting the midpoint of PQ to the midpoint of PR.
Calculate the coordinates of the midpoints as the mean values of the vertex endpoints.
The midpoint of PQ is (2,-8.5)
The midpoint of PR is (-1,-5.5)
The distance between those points is
sqrt(3^2 + 3^2) = sqrt18 = 4.24
To find the length of the midsegment connecting the midpoint of PQ to the midpoint of PR, we need to first find the coordinates of the midpoints of PQ and PR.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
Midpoint = ((x1 + x2) / 2 , (y1 + y2) / 2)
So, let's find the coordinates of the midpoints:
Midpoint of PQ = ((0 + 4) / 2 , (-8 + (-9)) / 2)
= (2, -8.5)
Midpoint of PR = ((0 + (-2)) / 2 , (-8 + (-3)) / 2)
= (-1, -5.5)
Now that we have the coordinates of the midpoints, we can find the length of the midsegment connecting them.
The length of a line segment with endpoints (x1, y1) and (x2, y2) is given by the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So, let's calculate the length of the midsegment:
Distance = sqrt((-1 - 2)^2 + (-5.5 - (-8.5))^2)
= sqrt((-3)^2 + (3)^2)
= sqrt(9 + 9)
= sqrt(18)
Therefore, the length of the midsegment connecting the midpoint of PQ to the midpoint of PR is sqrt(18).