Find the distance between the points R(0,5) and S(12,3). Round the answer to the nearest tenth.
We can use the distance formula to find the distance between the points R(0,5) and S(12,3).
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = 0, y1 = 5, x2 = 12, and y2 = 3. Substituting these values into the formula, we have:
d = sqrt((12 - 0)^2 + (3 - 5)^2)
= sqrt(144 + 4)
= sqrt(148)
≈ 12.2
Therefore, the distance between the points R(0,5) and S(12,3) is approximately 12.2.
An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip?
We can use the distance formula to find the distance between the points T(80,20), U(20,60), and V(110,85).
The distance between T and U is given by:
d1 = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((20 - 80)^2 + (60 - 20)^2)
= sqrt((-60)^2 + (40)^2)
= sqrt(3600 + 1600)
= sqrt(5200)
≈ 72.1
The distance between T and V is given by:
d2 = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((110 - 80)^2 + (85 - 20)^2)
= sqrt((30)^2 + (65)^2)
= sqrt(900 + 4225)
= sqrt(5125)
≈ 71.6
The distance between U and V is given by:
d3 = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((110 - 20)^2 + (85 - 60)^2)
= sqrt((90)^2 + (25)^2)
= sqrt(8100 + 625)
= sqrt(8725)
≈ 93.4
To find the shortest possible distance for the trip, we need to find the sum of the two shortest distances. In this case, that would be d1 + d3:
72.1 + 93.4 ≈ 165.5
Therefore, the shortest possible distance for the trip from T(80,20) to both U(20,60) and V(110,85) is approximately 165.5.
To find the distance between two points in a Cartesian plane, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given the points R(0,5) and S(12,3), we can substitute the values into the formula:
Distance = sqrt((12 - 0)^2 + (3 - 5)^2)
= sqrt((12)^2 + (-2)^2)
= sqrt(144 + 4)
= sqrt(148)
≈ 12.2
Therefore, the distance between points R(0,5) and S(12,3) is approximately 12.2 units.