Applying Distance Formula to Prove Some Geometric Properties

1. To prove whether a given triangle is equilateral or not, what formula will you use?

• A. Midpoint Formula

• B. Distance Formula

• C. Skype Formula

• D. Perimeter Formula

Three vertices of a square are (3,8), (15,8), and 3,-4). What are the coordinates of the fourth vertex?

• A. (-15, -4)

• B. (15, 4)

• C. (15, -4)

• D. (-15, 4)

What are the coordinates of point Y if YUMI is a square?

• A. (m, m)

• B. (m, 0)

• C. (-m, -m)

• D. (0, m)

4. The coordinates of the vertices of a triangle are M (-1, -3), A (7, 5), and Y (7, -2). What is the length of the segment joining vertices A and Y?

• A. 5

• B. 4

• C. 3

• D. 7

5. Which of the following statements will correctly describe the figure that will be formed when the points A(3, 7), B (11, 10), C (11, 5), and D (3, 2) are connected consecutively?

• A. The diagonals of the figure are congruent.

• B. The figure formed has 4 congruent angles.

• C. The figure formed has two pairs of opposite sides that are parallel.

• D. The figure formed has one pair of parallel sides.

6. The three of the vertices of a square are (−1,2),(3,2), and (1,0). What are the coordinates of the fourth vertex?

• A. (1, 4)

• B. (-1, 4)

• C. (-1, -4)

• D. (1, -4)

7. What figure is formed when the points 𝐷(−2,10), 𝐸(−2,−10), 𝐹(6,−10), and 𝐺(6,10) are connected consecutively?

• A. trapezoid

• B. parallelogram

• C. square

• D. rectangle

8. Three speed cameras were installed at different points along an expressway. On the map drawn on a coordinate plane, the coordinates of the first speed camera are (6,−4). Suppose the second camera is exactly between the other two and its coordinates are (−11,8), what are the coordinates of the third speed camera?

• A. (−28,−20)

• B. (28,−20)

• C. (28,20)

• D. (−28,20)

9. What are the coordinates of point 𝑌 if 𝐺𝐴𝑌 is an isosceles triangle?

• A. (0,0)

• B. (𝑠,0)

• C. (0,−𝑠)

• D. (−𝑠,0)

10. Triangle 𝐴𝐵𝐶 has the following vertices: 𝐴(2,−4),𝐵(3,−2), and 𝐶(2,0). What kind of triangle is Δ𝐴𝐵𝐶?

• A. equilateral

• B. right

• C. isosceles

• D. scalene