AST Geometry and Trigonometry 2

Question 1

What is the slope of a line passing through the points (2, 3) and (6, 11)?

Accepted Answer

2

Answer

Slope = (y₂−y₁)/(x₂−x₁) = (11−3)/(6−2) = 8/4 = 2.

Question 2

What is the distance between the points (1, 1) and (4, 5)?

Accepted Answer

5

Answer

Distance = √((4−1)² + (5−1)²) = √(9 + 16) = √25 = 5.

Question 3

What is the midpoint of the segment connecting (0, 4) and (6, 2)?

Accepted Answer

(3, 3)

Answer

Midpoint = ((0+6)/2, (4+2)/2) = (3, 3).

Question 4

What is the slope of a line perpendicular to y = 2x + 5?

Accepted Answer

−½

Answer

Perpendicular slopes are negative reciprocals; the negative reciprocal of 2 is −½.

Question 5

The equation x² + y² = 25 represents a circle with what radius?

Accepted Answer

5

Answer

The standard circle equation is x² + y² = r², so r = √25 = 5.

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