Distance Formula

Front

What is the Distance Formula used to calculate the distance between two points in a coordinate plane?

Back

The Distance Formula is written as d = √((x₂ - x₁)² + (y₂ - y₁)²).

Tags

CCSS.HSG.GPE.B.7

Front

How do you find the distance between the points (-2,-1) and (6,5) using the Distance Formula?

Back

Using the Distance Formula: d = √((6 - (-2))² + (5 - (-1))²) = √(8² + 6²) = √(64 + 36) = √100 = 10.

Tags

CCSS.HSG.GPE.B.7

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Tags

CCSS.8.EE.B.5

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The slopes of two perpendicular lines are negative reciprocals of each other.

Tags

CCSS.8.EE.B.6

Front

How do you determine if two lines are parallel, perpendicular, or neither?

Back

Compare the slopes of the lines: if they are equal, they are parallel; if their product is -1, they are perpendicular; otherwise, they are neither.

Tags

CCSS.HSG.GPE.B.6

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 3x - 3?

Back

The slope of the line is also 3.

Tags

CCSS.8.EE.B.5

Front

Given the equations y = -1/4 x - 5 and y = 4x + 2, are these lines parallel, perpendicular, or neither?

Back

These lines are perpendicular because their slopes (-1/4 and 4) are negative reciprocals.

Tags

CCSS.8.EE.B.6

Front

How do you calculate the distance between the points (8,8) and (3,-4) using the Distance Formula?

Back

Using the Distance Formula: d = √((3 - 8)² + (-4 - 8)²) = √((-5)² + (-12)²) = √(25 + 144) = √169 = 13.

Tags

CCSS.HSG.GPE.B.7

Front

What is the significance of the Distance Formula in geometry?

Back

The Distance Formula is significant because it allows for the calculation of the straight-line distance between two points in a Cartesian coordinate system.

Tags

CCSS.HSG.GPE.B.7