Coordinate Geometry

Front

What is the slope of a line parallel to the line given by the equation 2x - 3y = 11?

Back

The slope of a line parallel to the line 2x - 3y = 11 is \frac{2}{3}.

Front

What are the properties of the diagonals of a rhombus?

Back

The diagonals of a rhombus are perpendicular and bisected.

Front

How do you find the length of the diagonals of a rhombus?

Back

To find the length of the diagonals of a rhombus, use the formula: d1 = 2 * area / d2, where d1 and d2 are the lengths of the diagonals.

Front

What is the distance formula used to find the distance between two points A(x1, y1) and B(x2, y2)?

Back

The distance formula is given by: d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Front

Calculate the distance between the points A(8, 0) and B(2, -3).

Back

The distance between A(8, 0) and B(2, -3) is \sqrt{45}.

Front

What is the formula for the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as: m = \frac{y2 - y1}{x2 - x1}.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope.

Front

What is the relationship between the slopes of perpendicular lines?

Back

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

Front

How do you determine if a point lies on a line given by an equation?

Back

To determine if a point (x, y) lies on a line, substitute the x-value into the equation and check if the resulting y-value matches the y-coordinate of the point.