12345 - Math Quiz -Geometry Covering: geometric concepts such as lines, angles, triangles, quadrilaterals, circles, and various coordinate geometry topics, including the distance formula, midpoint formula, and slope. 1 / 5 1. A right-angled triangle has hypotenuse of length 15 and one leg of length 9. What is the length of the other leg? a) 5 b) 6 c) 8 d) 12 Using the Pythagorean theorem (a² + b² = c²), we can solve for the length of the other leg. Let a represent one leg of the triangle, b represent the other leg, and c represent the hypotenuse. We are given that the hypotenuse has length 15 (c = 15) and one leg has length 9 (a = 9). We need to find the other leg (b). 9² + b² = 15² 81 + b² = 225 Subtract 81 from both sides: b² = 144 Taking the square root of both sides: b = 12 So, the length of the other leg is 12. The correct answer is D) 12. 2 / 5 2. If the ratio of the measures of two complementary angles is 3:2, what is the measure of the smaller angle? a) 36° b) 45° c) 54° d) 62° Complementary angles are angles whose measures add up to 90°. Let's call the measures of the two complementary angles 3x and 2x. Thus, the equation can be written as: 3x + 2x = 90 5x = 90 Dividing both sides by 5 to solve for x: x = 18 Now we substitute x back into 2x, which represents the measure of the smaller angle: 2(18) = 36 So, the measure of the smaller angle is 36°. The correct answer is A) 36°. 3 / 5 3. In the coordinate plane, the endpoints of the diameter of a circle are (3, 7) and (9, 1). Find the coordinates of the center of the circle. a) (6, 4) b) (6, 3) c) (5, 4) d) (4, 3) The midpoint of the diameter of a circle is the center of the circle. To find the coordinates of the center, we can use the midpoint formula: (midpoint_x, midpoint_y) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) Given the endpoints are (3, 7) and (9, 1), we have: midpoint_x = (3 + 9) / 2 = 12 / 2 = 6 midpoint_y = (7 + 1) / 2 = 8 / 2 = 4 The coordinates of the center of the circle are (6, 4). The correct answer is A) (6, 4). 4 / 5 4. What is the circumference of a circle with a diameter of 10 inches? a) 5π b) 10π c) 20π d) 25π To find the circumference of a circle, we can use the formula: Circumference = π × diameter Given the diameter of the circle is 10 inches, we have: Circumference = π × 10 So, the circumference of the circle is 10π inches. The correct answer is B) 10π. 5 / 5 5. Which of the following is the equation of a circle with center (2, -3) and radius 5? a) (x - 2)² + (y + 3)² = 25 b) (x + 2)² + (y - 3)² = 25 c) (x - 2)² + (y + 3)² = 5 d) (x + 2)² + (y - 3)² = 5 The standard equation of a circle in coordinate geometry is given by (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. In the given question, the center of the circle is (2, -3) and the radius is 5. So, we have h = 2, k = -3, and r = 5. Now, we can plug these values into the standard equation of the circle: (x - 2)² + (y + 3)² = 5² (x - 2)² + (y + 3)² = 25 So, the correct answer is A) (x - 2)² + (y + 3)² = 25. Your score is 0% Restart Quiz
