NJGPA Applying Geometric Theorems 5

Question 1

In the coordinate plane, points A(1, 2), B(5, 2), and C(5, 6) form a right triangle. What is the distance from A to C?

Accepted Answer

4√2

Answer

Using the distance formula: AC = √((5−1)² + (6−2)²) = √(16 + 16) = √32 = 4√2.

Question 2

A diagonal of a square has length 8√2. What is the side length of the square?

Accepted Answer

8

Answer

For a square with side s, the diagonal = s√2, so s = 8√2 ÷ √2 = 8.

Question 3

In an equilateral triangle, each side has length 6. What is the height of the triangle?

Accepted Answer

3√3

Answer

The height of an equilateral triangle with side s is (s√3)/2 = (6√3)/2 = 3√3.

Question 4

Two secants are drawn from external point P. The near and far intersections of the first secant are 3 and 8 from P; the near intersection of the second secant is 4 from P. What is the far intersection of the second secant from P?

Accepted Answer

6

Answer

By the Secant-Secant Theorem: 3 × 8 = 4 × x, so 24 = 4x, giving x = 6.

Question 5

In triangle ABC, angle bisectors from A, B, and C meet at point I. This point I is called the:

Accepted Answer

Incenter

Answer

The incenter is the point where the three angle bisectors of a triangle intersect and is equidistant from all three sides.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

NJGPA Applying Geometric Theorems 5