Midpoints and Distance on the Coordinate Plane

Midpoints and Distance on the Coordinate Plane

Midpoint between Two Points on the Coordinate Plane

Midpoint on a Number Line

• The midpoint between two numbers on a number line is a point that is equidistant from the endpoints and divides the segment into 2 congruent segments

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Midpoint on a Number Line

• To find the midpoint of two numbers on the number line you add the endpoints and divide by 2

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Midpoint between Two Points on the Coordinate Plane

• A point on the coordinate plane has a horizontal distance (x-value) and a vertical distance (y-value)

• We take both of those in consideration when finding the midpoint

Midpoint between Two Points on the Coordinate Plane

• To find the midpoint between two points on the coordinate plane you find the midpoint of the x-values and the midpoint of the y-values

• To find the midpoint of the x-values, add them and divide by 2

• To find the midpoint of the y-values, add them and divide by 2

Find the midpoint between (2, 5) and (8, 15)

• x values are 2 and 8. Add 2 + 8 and then divide by 2. 2 + 8 = 10, 10/2 = 5. The x value of the midpoint is 5.

• y values are 5 and 15. Add 5 + 15 and then divide by 2. 5 + 15 = 20, 20/2 = 10. The y value of the midpoint is 10.

• The midpoint is (5, 10)

Find the midpoint between (-7, 15) and (11, -4).

• the x-values are -7 and 11. Add -7 + 11 = 4. 4/2 = 2. The x value of the midpoint is 2.

• the y-values are 15 and -4. Add 15 and -4. 15 + (-4) = 11. 11/2 = 5.5. The y value of the midpoint is 5.5

• The midpoint is (2, 5.5)

Multiple Choice

Find the coordinates of the midpoint A(−5, 4) and B(−5, 18)

• (2, 9.5)

• (−5, 11)

• (5.5, 0)

• (−3.5, 3)

Multiple Choice

Find the coordinates of the midpoint E(4, 11) and F(−11, −5)

• (2, 9.5)

• (−3.5, 3)

• (−5, 11)

• (5.5, 0)

Multiple Choice

Find the coordinates of the midpoint Q(−3, 14) and R(7, 5)

• (2, 9.7)

• (9, 2.5)

• (4, 2.5)

• (2, 9.5)

Multiple Choice

Find the coordinates of the midpoint Q(−3, 14) and R(7, 5)

• (2, 9.7)

• (9, 2.5)

• (4, 2.5)

• (2, 9.5)

Distance between Two Points on the Number Line

• The distance between two points on the number line is measured in absolute value.

• The distance is always positive, but we can be traveling in a "negative" direction, as in going to school and coming home from school. Same distance, different direction.

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Distance between Two Points on the Number Line

• To find the distance between two points on the number line we take the absolute value of the difference of the two points

• | p₂ - p₁ |

Distance between Two Numbers in the Coordinate Plane

• Numbers in the coordinate plane have a horizontal distance and a vertical distance

• To find the distance between the 2 points we have to take that into consideration.

• We also have to remember that distance is a positive value

Distance between Two Points on the Coordinate Plane

• The distance formula is derived from the pythagorean theorem

• Horizontal difference is one side of the right triangle (subtract x-values)

• Vertical difference is another side of the righ triangle (subtract y-values

• Hypotenuse is the distance between the points

• c ²= a² + b²

Distance between Two Points in the Coordinate Plane

• To find the distance between two points take the square root of the sum of the difference between the x-values squared and the difference between the y-values squared.

Multiple Choice

What is the distance between points (-7, 8) and (2, 8)?

• 4 units
• 5 units
• 3 units
• 9 units

Multiple Choice

What is the distance between (-5, 5) and (1, -2)

• 9.2

• 12.6

• 14

• 7.8

Multiple Choice

Find the distance between (3, 24) and (7, 56).

• 32.1

• 32.2

• 32.3

• 32.4

Multiple Choice

Find the distance between (-9, -1) and (-2, -6).Round to the nearest tenth.

• 8.6

• 12.1

• 9.9

• 13.0