Unit 4 Review

Front

What is the formula to find the midpoint of a line segment connecting two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right).

Front

Given points A(-2, 7) and B(6, -5), what is the midpoint?

Back

M = \left(\frac{-2 + 6}{2}, \frac{7 - 5}{2}\right) = \left(2, 1\right).

Front

If the midpoint M(4, 3) and one endpoint G(5, -6) are known, how do you find the other endpoint H(x, y)?

Back

Use the formula: M = \left(\frac{x + 5}{2}, \frac{y - 6}{2}\right). Solve for x and y.

Front

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

Back

The slope m is calculated as m = \frac{y_2 - y_1}{x_2 - x_1}.

Front

Find the slope of the line through points (1, 2) and (3, 6).

Back

m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 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

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

Back

The equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

If a line has a slope of 5 and passes through the point (0, 4), what is its equation?

Back

The equation is y = 5x + 4.

Front

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

Back

The distance d is given by d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Front

Find the distance between points J(1, 2) and K(4, 6).

Back

d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.