Question

1.Find the coordinates of the midpoint of __ given that H (-1,3) and X (7,1).

HX

A.(3,1)
B (0,4)
C(-3,1)
D(-4,0)

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

A 10.4
B 16
C 12.2
D 11.8

3. 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?

A. 165 units
B. 170 units
C. 97 units
D. 169 units

Answer 1

1. B. 2.C 3.C.    these answers are all correct.

Answer 2

1. (3, 2)

2. Option C. 12.2

3. Option A. 165 units

Explanation:

1. The midpoint of two coordinates (x₁, x₂) and (y₁, y₂) is calculate by,

`(x, y) = ((x_(1) + x_(2))/(2),(y_(1) + y_(2))/(2))`

⇒
`(x, y) = ((-1 + 7)/(2),(3 + 1)/(2))`

Thus (x, y) = (3, 2)

Hence, none of given options are true.

2. The distance between two coordinates is calculate by,

`Distance=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2`

⇒ Distance = 12.16 ≈ 12.2 unit

Hence, option (C) is correct.

3. The distance between T(80, 20) and V(110, 85) is comparatively smaller than T(80, 20) and U(20, 60).

Using the Distance formula,

`Distance=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2`

Distance between T(80, 20) and V(110, 85) is 71.59 unit

and Distance between U(20, 60) and V(110, 85) is 93.41 unit

So, Airplane firstly go to point V from point T and then point U.

Total shortest distance = 71.60 + 93.40 = 165 unit.

Hence, option (A) is correct.