NJGPA Algebra I and Geometry Concepts 5

Question 1

What is the distance between the points (-3, 1) and (1, 4)?

Accepted Answer

5

Answer

Distance = √((1-(-3))² + (4-1)²) = √(16 + 9) = √25 = 5.

Question 2

A line has equation 4x - 2y = 8. What is its slope?

Accepted Answer

2

Answer

Rewrite in slope-intercept form: -2y = -4x + 8, so y = 2x - 4; the slope is 2.

Question 3

An exterior angle of a triangle measures 120°. One of the non-adjacent interior angles is 45°. What is the other non-adjacent interior angle?

Accepted Answer

75°

Answer

An exterior angle equals the sum of the two non-adjacent interior angles: 45 + x = 120, so x = 75°.

Question 4

Which set of numbers could be the side lengths of a right triangle?

Accepted Answer

6, 8, 10

Answer

Check: 6² + 8² = 36 + 64 = 100 = 10², confirming a right triangle.

Question 5

Factor completely: 2x² + 8x

Accepted Answer

2x(x + 4)

Answer

Factor out the GCF of 2x: 2x² + 8x = 2x(x + 4).

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test