Question

Find the distance between the points R(0,5) and S(12,3). Round the answer to the nearest tenth.

Answer 1

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?

Answer 2

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.

Answer 3

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.