Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the concepts of midpoint and distance in the coordinate plane. It explains how to find the midpoint on a number line and within a coordinate plane using averages. The distance formula is introduced, showing its basis in the Pythagorean theorem. The video includes three examples: finding a midpoint, solving for a missing endpoint, and calculating the distance between two points. These examples help reinforce the understanding of the formulas and their applications.

What are the two main topics discussed in this video?

• Volume and Surface Area

• Slope and Intercept

• Midpoint and Distance

• Area and Perimeter

Tags

CCSS.8.EE.B.5

How do you find the midpoint on a number line?

• Subtract the smaller point from the larger point

• Add the two points and divide by two

• Divide the larger point by the smaller point

• Multiply the two points

Tags

CCSS.HSN.CN.B.6

In a coordinate plane, how do you find the midpoint?

• Divide the x-coordinates by the y-coordinates

• Multiply the x-coordinates and the y-coordinates

• Subtract the y-coordinates from the x-coordinates

• Find the average of the x-coordinates and the y-coordinates

Tags

CCSS.HSG.GPE.B.6

What theorem is the distance formula based on?

• Pythagorean theorem

• Binomial theorem

• Fundamental theorem of calculus

• Euclidean algorithm

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CCSS.HSG.GPE.B.7

Why do we square the differences in the distance formula?

• To convert the values to integers

• To make the values smaller

• To ensure the differences are positive

• To make the calculation easier

Tags

CCSS.HSG.GPE.B.7

What is the formula for the distance between two points?

• d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

• d = (x2 - x1) * (y2 - y1)

• d = (x2 - x1) + (y2 - y1)

• d = (x2 - x1)^2 + (y2 - y1)^2

Tags

CCSS.HSG.GPE.B.7

What is the midpoint between -4 and 9 on a number line?

• 2.5

• 0.5

• 5

• 1.5

Tags

CCSS.HSN.CN.B.6

If the midpoint is (-2, 1) and one endpoint is (-5, 7), what is the x-coordinate of the missing endpoint?

• 4

• 3

• 2

• 1

Tags

CCSS.HSG.GPE.B.6

If the midpoint is (-2, 1) and one endpoint is (-5, 7), what is the y-coordinate of the missing endpoint?

• -3

• -5

• -6

• -4

Tags

CCSS.HSG.GPE.B.6

What is the distance between the points (4, -3) and (-7, 5) rounded to the nearest tenth?

• 13.6

• 15.1

• 14.2

• 12.3

Tags

CCSS.HSG.GPE.B.7