Semester Midpoints, Distance & the Coordinate Plane (S1)

Front

What is the midpoint formula for 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

Find the midpoint of line segment AB, given A (7, 2) and B (6, -2).

Back

M = \left(\frac{7 + 6}{2}, \frac{2 + (-2)}{2}\right) = \left(\frac{13}{2}, 0\right).

Front

What is the slope of a line given by the equation 3x + 7y = 35?

Back

To find the slope, rewrite in slope-intercept form (y = mx + b): 7y = -3x + 35, so y = -\frac{3}{7}x + 5. The slope m = -\frac{3}{7}.

Front

What is the distance formula 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 the points (1, 2) and (4, 6).

Back

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

Front

What is the slope of a line that rises 4 units for every 1 unit it runs?

Back

The slope m = \frac{rise}{run} = \frac{4}{1} = 4.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

If a line has a slope of -2, what does this indicate about the line's direction?

Back

A slope of -2 indicates that the line falls as it moves from left to right.

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 (x=0).

Front

Find the slope of the line passing through the points (2, 3) and (5, 11).

Back

m = \frac{11 - 3}{5 - 2} = \frac{8}{3}.