|
TestingSnehilCoorGeo 20 Flashcards 
|
|
|
Card: 1 / 20 
|
What is the distance formula between two points? |
|
|
Card: 2 / 20
|
The distance between two points (x₁, y₁) and (x₂, y₂) is √((x₂ - x₁)² + (y₂ - y₁)²). For example, the distance between (2, 3) and (5, 7) is √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5. |
|
|
Card: 3 / 20
|
What is the midpoint formula for two points? |
|
|
Card: 4 / 20
|
The midpoint M of a line segment connecting points (x₁, y₁) and (x₂, y₂) is given by M = ((x₁ + x₂)/2, (y₁ + y₂)/2). For example, the midpoint of (1, 2) and (3, 4) is M = ((1 + 3)/2, (2 + 4)/2) = (2, 3). |
|
|
Card: 5 / 20
|
How can you determine if two lines are parallel? |
|
|
Card: 6 / 20
|
Two lines are parallel if their slopes are equal. For example, if line 1 has a slope of m₁ and line 2 has a slope of m₂, then if m₁ = m₂, the lines are parallel. |
|
|
Card: 7 / 20
|
Calculate the area of a triangle with vertices at (0, 0), (4, 0), and (0, 3). |
|
|
Card: 8 / 20
|
The area A of a triangle with vertices at (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by A = ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|. For the given points: A = ½ |0(0 - 3) + 4(3 - 0) + 0(0 - 0)| = ½ |0 + 12 + 0| = 6. |
|
|
Card: 9 / 20
|
What is the formula for the slope of a line given two points? |
|
|
Card: 10 / 20
|
The slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is given by m = (y₂ - y₁) / (x₂ - x₁). For example, for points (2, 3) and (5, 7), m = (7 - 3) / (5 - 2) = 4 / 3. |
|
|
Card: 11 / 20
|
What is the standard equation of a circle with center (h, k) and radius r? |
|
|
Card: 12 / 20
|
The standard equation of a circle is (x - h)² + (y - k)² = r². For example, for a circle centered at (1, -2) with radius 4, the equation is (x - 1)² + (y + 2)² = 16. |
|
|
Card: 13 / 20
|
Find the coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), and (6, 1). |
|
|
Card: 14 / 20
|
The centroid G of a triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃) is given by G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3). Here, G = ((2 + 4 + 6)/3, (3 + 5 + 1)/3) = (4, 3). |
|
|
Card: 15 / 20
|
What is the area of a triangle with vertices at (3, 4), (5, 11), and (12, 8)? |
|
|
Card: 16 / 20
|
Using the area formula A = ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|, we find A = ½ |3(11 - 8) + 5(8 - 4) + 12(4 - 11)| = ½ |9 + 20 - 84| = ½ | -55 | = 27.5. |
|
|
Card: 17 / 20
|
What is the equation of a line in slope-intercept form given a slope of 2 and a y-intercept of -3? |
|
|
Card: 18 / 20
|
The equation of the line is y = 2x - 3. This means for every unit increase in x, y increases by 2. |
|
|
Card: 19 / 20
|
Two lines intersect at point (1, 1) with slopes 2 and -1. What is the area of the triangle formed by these lines and the x-axis? |
|
|
Card: 20 / 20
|
To find the area, determine the x-intercepts of both lines. For the line y = 2x - 1 (slope 2), setting y = 0 gives x = ½. For the line y = -x + 2 (slope -1), setting y = 0 gives x = 2. The base of the triangle on the x-axis is from (½, 0) to (2, 0), which is 2 - ½ = 1.5. The height is 1 (y-coordinate of intersection). Thus, area = ½ * base * height = ½ * 1.5 * 1 = 0.75. |
|
|
|
 Completed! Keep practicing to master all of them. |
|
