ACT Coordinate Geometry

Front

What is the axis of symmetry?

Back

The axis of symmetry is a line that divides a figure into two mirror-image halves. For a parabola, it is the vertical line that passes through the vertex.

Front

Describe the transformation from the graph of f to the graph of g if g is a vertical translation 2 units up of f.

Back

This means that every point on the graph of f is moved vertically upwards by 2 units to create the graph of g.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if they intersect at a right angle (90 degrees). The slopes of perpendicular lines are negative reciprocals of each other.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase. It is decreasing if its output values fall as the input values increase.

Front

How can you determine if two lines are parallel?

Back

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

Front

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

Back

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

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, indicating the value of y when x is 0.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is a vertical translation in graph transformations?

Back

A vertical translation moves a graph up or down without changing its shape.

Front

What is a horizontal translation in graph transformations?

Back

A horizontal translation moves a graph left or right without changing its shape.