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5 questions

GAME 2002

Mountain View College

1. What is the result of adding the two-dimensional vectors (3, 4) and (-1, 2)?
Answer and explanation

(2, 6)

Add corresponding components: 3 + (-1) = 2 for the x-component, and 4 + 2 = 6 for the y-component.

2. What is the straight-line distance between the points (1, 2) and (4, 6)?
Answer and explanation

5 units

Using the distance formula, √((4 − 1)² + (6 − 2)²) = √(3² + 4²) = √25 = 5 units.

3. A unit direction vector points at an angle of 60° measured counterclockwise from the positive x-axis. What are its horizontal and vertical components?
Answer and explanation

(1/2, √3/2)

For an angle measured from the positive x-axis, the horizontal component is cos(θ) and the vertical component is sin(θ). Since cos(60°) = 1/2 and sin(60°) = √3/2, the components are (1/2, √3/2).

4. In a linear interpolation from A = 10 to B = 30, what value does t = 0.25 produce?
Answer and explanation

15

Using A + t(B − A), the result is 10 + 0.25(30 − 10) = 10 + 5 = 15.

5. In a 2D game coordinate system, an object is at (4, 7). If its x-coordinate changes to 9 while its y-coordinate stays the same, how does the object’s position change?
Answer and explanation

It moves horizontally, with y remaining 7.

Changing x affects horizontal position, while leaving y unchanged keeps the vertical position at 7.