Q. If the coordinates of points A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the area of triangle ABC?
Show solution
Solution
Area = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| = 1/2 * |1(6-2) + 4(2-2) + 7(2-6)| = 1/2 * |4 + 0 - 28| = 12.
Correct Answer:
B
— 10
Learn More →
Q. If the coordinates of the center of a circle are (0, 0) and it passes through the point (3, 4), what is the radius of the circle?
A.
3 units
B.
4 units
C.
5 units
D.
7 units
Show solution
Solution
Radius = distance from center to point = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5 units.
Correct Answer:
C
— 5 units
Learn More →
Q. If the coordinates of the center of a circle are (2, 3) and the radius is 4, what is the equation of the circle?
A.
(x - 2)² + (y - 3)² = 16
B.
(x + 2)² + (y + 3)² = 16
C.
(x - 2)² + (y + 3)² = 16
D.
(x + 2)² + (y - 3)² = 16
Show solution
Solution
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x - 2)² + (y - 3)² = 16
Learn More →
Q. If the coordinates of the center of a circle are (3, 4) and the radius is 5, what is the equation of the circle?
A.
(x-3)² + (y-4)² = 25
B.
(x+3)² + (y+4)² = 25
C.
(x-3)² + (y-4)² = 5
D.
(x-3)² + (y-4)² = 20
Show solution
Solution
The standard form of the equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x-3)² + (y-4)² = 25
Learn More →
Q. If the coordinates of the center of a circle are (4, -2) and it passes through the point (4, 2), what is the radius of the circle?
Show solution
Solution
Using the distance formula: radius = √((4 - 4)² + (2 - (-2))²) = √(0 + 16) = √16 = 4.
Correct Answer:
B
— 2
Learn More →
Q. If the coordinates of the vertices of a triangle are (0, 0), (4, 0), and (0, 3), what is the area of the triangle?
A.
6 square units
B.
12 square units
C.
8 square units
D.
10 square units
Show solution
Solution
The area of a triangle can be calculated using the formula A = 1/2 * base * height. Here, base = 4 and height = 3, so A = 1/2 * 4 * 3 = 6 square units.
Correct Answer:
A
— 6 square units
Learn More →
Q. If the coordinates of the vertices of a triangle are (0, 0), (4, 0), and (0, 3), what is the perimeter of the triangle?
Show solution
Solution
The lengths of the sides are 4, 3, and 5 (using the Pythagorean theorem). Therefore, the perimeter = 4 + 3 + 5 = 12.
Correct Answer:
A
— 12
Learn More →
Q. If the coordinates of the vertices of a triangle are (0,0), (4,0), and (0,3), what is its area?
A.
6 cm²
B.
12 cm²
C.
8 cm²
D.
10 cm²
Show solution
Solution
The area of a triangle can be calculated using the formula A = 1/2 * base * height. Here, base = 4 cm and height = 3 cm, so A = 1/2 * 4 * 3 = 6 cm².
Correct Answer:
A
— 6 cm²
Learn More →
Q. If the coordinates of the vertices of a triangle are (1, 1), (4, 1), and (1, 5), what is the length of the base?
Show solution
Solution
The base is the distance between (1, 1) and (4, 1): d = √((4-1)² + (1-1)²) = √9 = 3.
Correct Answer:
A
— 3
Learn More →
Q. If the coordinates of the vertices of a triangle are A(1, 1), B(4, 1), and C(1, 5), what is the perimeter of the triangle?
Show solution
Solution
Length AB = 3, Length AC = 4, Length BC = √((4-1)² + (1-5)²) = √(9 + 16) = 5. Perimeter = 3 + 4 + 5 = 12.
Correct Answer:
B
— 12
Learn More →
Q. If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the length of side AB?
Show solution
Solution
Length AB = √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
Learn More →
Q. If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the perimeter of the triangle?
Show solution
Solution
Perimeter = AB + BC + CA = √((4-1)² + (5-1)²) + √((7-4)² + (2-5)²) + √((1-7)² + (1-2)²) = 3 + √(9 + 9) + √(36 + 1) = 3 + 4.24 + 6.08 = 13.32.
Correct Answer:
B
— 14
Learn More →
Q. If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1, 6), what is the area of the triangle?
A.
6 square units
B.
8 square units
C.
10 square units
D.
12 square units
Show solution
Solution
Using the formula Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|, we find Area = 1/2 |1(6 - 6) + 4(6 - 2) + 1(2 - 6)| = 1/2 |0 + 16 - 4| = 1/2 * 12 = 6 square units.
Correct Answer:
A
— 6 square units
Learn More →
Q. If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(1, 6), what is the base of the triangle AB?
Show solution
Solution
Base AB = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 3
Learn More →
Q. If the coordinates of the vertices of a triangle are A(1, 2), B(4, 6), and C(7, 2), what is the perimeter of the triangle?
Show solution
Solution
Perimeter = AB + BC + CA = √((4-1)² + (6-2)²) + √((7-4)² + (2-6)²) + √((1-7)² + (2-2)²) = 3 + 5 + 6 = 14.
Correct Answer:
B
— 14
Learn More →
Q. If the coordinates of the vertices of triangle ABC are A(1, 2), B(4, 6), and C(1, 6), what is the length of side AB?
Show solution
Solution
Using the distance formula, AB = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.
Correct Answer:
B
— 4
Learn More →
Q. If the coordinates of the vertices of triangle PQR are P(1, 2), Q(4, 6), and R(1, 6), what is the length of side PQ?
Show solution
Solution
Using the distance formula, PQ = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.
Correct Answer:
B
— 4
Learn More →
Q. If the data set is 10, 20, 30, 40, 50, what is the mean?
Show solution
Solution
Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30
Correct Answer:
A
— 30
Learn More →
Q. If the data set is: 10, 20, 30, 40, 50, what is the variance?
A.
100
B.
200
C.
250
D.
300
Show solution
Solution
Mean = 30; Variance = [(10-30)² + (20-30)² + (30-30)² + (40-30)² + (50-30)²] / 5 = 200.
Correct Answer:
C
— 250
Learn More →
Q. If the diagonals of a rectangle are 10 cm long, what is the length of each side if the rectangle is a square?
A.
5 cm
B.
10 cm
C.
7.07 cm
D.
8 cm
Show solution
Solution
In a square, the diagonal d is related to the side length s by the formula d = s√2. Therefore, s = d/√2 = 10 cm/√2 = 10 cm/1.414 ≈ 7.07 cm.
Correct Answer:
C
— 7.07 cm
Learn More →
Q. If the diagonals of a rhombus are 10 cm and 24 cm, what is the area of the rhombus?
A.
120 cm²
B.
60 cm²
C.
80 cm²
D.
100 cm²
Show solution
Solution
The area of a rhombus can be calculated using the formula: Area = 1/2 × d1 × d2, where d1 and d2 are the lengths of the diagonals. Therefore, Area = 1/2 × 10 cm × 24 cm = 120 cm².
Correct Answer:
A
— 120 cm²
Learn More →
Q. If the diagonals of a rhombus are 10 cm and 24 cm, what is the area?
A.
120 cm²
B.
240 cm²
C.
300 cm²
D.
480 cm²
Show solution
Solution
The area of a rhombus can be calculated using the formula (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals. Here, area = (1/2) × 10 cm × 24 cm = 120 cm².
Correct Answer:
A
— 120 cm²
Learn More →
Q. If the diagonals of a rhombus are 12 cm and 16 cm, what is the area of the rhombus?
A.
96 cm²
B.
48 cm²
C.
192 cm²
D.
64 cm²
Show solution
Solution
The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2. Here, d1 = 12 cm and d2 = 16 cm, so Area = (12 * 16) / 2 = 96 cm².
Correct Answer:
A
— 96 cm²
Learn More →
Q. If the diagonals of a rhombus are 6 cm and 8 cm, what is its area?
A.
24 cm²
B.
30 cm²
C.
36 cm²
D.
48 cm²
Show solution
Solution
The area of a rhombus is calculated as (d1 × d2) / 2, where d1 and d2 are the lengths of the diagonals. Thus, the area is (6 cm × 8 cm) / 2 = 24 cm².
Correct Answer:
A
— 24 cm²
Learn More →
Q. If the diagonals of a rhombus are 6 cm and 8 cm, what is the area of the rhombus?
A.
24 cm²
B.
30 cm²
C.
48 cm²
D.
60 cm²
Show solution
Solution
The area of a rhombus can be calculated using the formula (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. Thus, the area is (6 cm * 8 cm) / 2 = 24 cm².
Correct Answer:
A
— 24 cm²
Learn More →
Q. If the diagonals of a rhombus are 8 cm and 6 cm, what is the area?
A.
24 cm²
B.
48 cm²
C.
36 cm²
D.
30 cm²
Show solution
Solution
The area of a rhombus can be calculated using the formula (d1 × d2) / 2, where d1 and d2 are the lengths of the diagonals. Here, area = (8 cm × 6 cm) / 2 = 24 cm².
Correct Answer:
A
— 24 cm²
Learn More →
Q. If the diameter of a circle is 10 cm, what is the area of the circle?
A.
25π cm²
B.
50π cm²
C.
100π cm²
D.
75π cm²
Show solution
Solution
The radius r = diameter/2 = 10/2 = 5 cm. The area A = πr² = π(5)² = 25π cm².
Correct Answer:
A
— 25π cm²
Learn More →
Q. If the diameter of a circle is 10 cm, what is the circumference of the circle?
A.
31.4 cm
B.
20 cm
C.
15.7 cm
D.
25 cm
Show solution
Solution
The circumference of a circle is given by the formula C = πd. For d = 10 cm, C = π(10) ≈ 31.4 cm.
Correct Answer:
A
— 31.4 cm
Learn More →
Q. If the diameter of a circle is 10 cm, what is the circumference?
A.
31.4 cm
B.
25.0 cm
C.
15.7 cm
D.
20.0 cm
Show solution
Solution
The circumference of a circle is given by C = πd. Here, C = π(10) ≈ 31.4 cm.
Correct Answer:
A
— 31.4 cm
Learn More →
Q. If the diameter of a circle is 12 cm, what is its area?
A.
113.04 cm²
B.
36 cm²
C.
144 cm²
D.
28.26 cm²
Show solution
Solution
Radius = diameter / 2 = 12 / 2 = 6 cm. Area = πr² = π(6)² = 36π ≈ 113.04 cm².
Correct Answer:
A
— 113.04 cm²
Learn More →
Showing 541 to 570 of 2594 (87 Pages)
