Midpoint and Distance

Front

What is the Midpoint Formula?

Back

The Midpoint Formula is used to find the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2). It is given by: M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right).

Front

How do you find the distance between two points (x1, y1) and (x2, y2)?

Back

The Distance Formula is used to find the distance d between two points and is given by: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

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.

Front

Write the equation of a line parallel to y = 2x + 3 that passes through the point (1, 4).

Back

The equation is y = 2x + 2.

Front

What is the slope of the line represented by the equation y = (-3/5)x - 3?

Back

The slope of the line is -3/5.

Front

Find the midpoint of the points (3, 9) and (-1, -5).

Back

The midpoint is (1, 2).

Front

Calculate the distance between the points (3, 7) and (-5, -8).

Back

The distance is 17.

Front

What is the formula for the length of a line segment?

Back

The length of a line segment can be found using the Distance Formula: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Front

If a line has a slope of 0, what type of line is it?

Back

A line with a slope of 0 is a horizontal line.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.