Dilation and Partitioning of Lines

The video tutorial covers dilating lines and partitioning line segments. It explains how to dilate a line by multiplying the y-intercept by a scale factor while keeping the slope constant, resulting in parallel lines. The concept of scale factor is discussed, emphasizing the 'new over old' rule. The tutorial also provides a detailed walkthrough of partitioning a line segment into a given ratio, including plotting points and calculating changes in coordinates. Several practice problems from Common Core tests are solved to reinforce these concepts.

When dilating a line, which part of the line equation is affected by the scale factor?

• The y-intercept

• The x-coefficient

• The entire equation

• The slope

If a line y = 3x + 5 is dilated by a scale factor of 3, what is the new y-intercept?

• 5

• 15

• 3

• 8

How is the scale factor determined when dilating a line?

• Difference between new and old y-intercepts

• New y-intercept divided by old y-intercept

• Old y-intercept divided by new y-intercept

• Sum of new and old y-intercepts

What is the first step in partitioning a line segment?

• Determine the scale factor

• Calculate the slope

• Plot the given points

• Find the midpoint

In partitioning a line segment, what does the ratio 1:3 indicate?

• One part from A, three parts from B

• Equal parts from A and B

• No parts from A, all from B

• Three parts from A, one part from B

What is the key concept to remember when dilating lines?

• New slope, same y-intercept

• Same slope and y-intercept

• Same slope, new y-intercept

• New slope and y-intercept

When solving for a dilated line, why is it important to convert the equation to y = mx + b form?

• To easily identify the slope

• To simplify the equation

• To find the x-intercept

• To apply the scale factor correctly

In a partitioning problem, if the direction is from B to A, how should you move?

• Towards the right and down

• Towards the left and down

• Towards the left and up

• Towards the right and up

What is the result of a dilation on the slope of a line?

• The slope is doubled

• The slope remains unchanged

• The slope is halved

• The slope becomes zero

In partitioning a line segment, what does the term 'change in x' refer to?

• The difference in y-coordinates

• The difference in x-coordinates

• The sum of x-coordinates

• The average of x-coordinates