1.9 Distance and Midpoint Formula; Circles

​1.9 Distance and Midpoint; Circles

​"Success is the sum of Small Efforts repeated day in and day out."

​- R. Collier

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Multiple Choice

The distance between A(3,1) and B(-2,-1) written correctly is: #1

• $$d=\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$$

• $$d=\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$$

• $$d=\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

• $$d=\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

Multiple Choice

Find the distance between the points (4, 3) and (0,6). #2

• 3

• 4

• 5

• 7

Fill in the Blanks

Multiple Choice

Find the distance between the pair of points R(-4, 1) and F(0, -2). #6

• 5

• 8.60

• 7

• 9.22

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Multiple Choice

What is the midpoint between (3, -1) and (8, -6)? #12

• (11, -7)

• (-5.5, -3.5)

• (5.5, -3.5)

• (2, -2)

Multiple Choice

Find the midpoint of the line segment joining the points P1 and P2. #13

P1 = (-4, -3); P2 = (2, 2)

• $$\left(-1,-\frac{1}{2}\right)$$

• $$\left(1,\frac{1}{2}\right)$$

• $$\left(1,-\frac{1}{2}\right)$$

• $$\left(-1,\frac{1}{2}\right)$$

Multiple Choice

Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14). #15

• (-1, 13)
• (13, 1)
• (13, -1)
• (5, 13)

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Multiple Choice

In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x² + y² = r².

If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?

#22

• (h + x)² + (k + y)² = r²

• (x – h)² + (y – k)² = r²

• k + x)² + (h + y)² = r²

• (x – k)² + (y – h)² = r²

Multiple Choice

What are the coordinates of the center and the radius of the circle with the equation:

(x - 4)² + (y - 3)² = 25 ? #23

• Center (4,3)

  Radius = 5 units

• Center (4,3)

  Radius = 25 units

• Center (-4,-3)

  Radius = 25 units

• Center (-4,-3)

  Radius = 5 units

Multiple Choice

What is the equation of the circle, with center (-2,-7) and radius 3 units? #24

• (x + 2)² + (y + 7)² = 3

• (x - 2)² + (y - 7)² = 9

• (x + 2)² + (y + 7)² = 9

• (x - 2)² + (y - 7)² = 3

Multiple Choice

Which graph corresponds to

x²+ (y-6)²=9? #26

• A

• B

• C

• D

Multiple Choice

Which graph corresponds to

(x-4)²+ (y+4)²=25? #27

• A

• B

• C

• D

Completing the Square

Why do we sometimes need to complete the square?

Multiple Choice

What is the center of a circle whose equation is x² + y² – 12x – 2y + 12 = 0? #29

• (–12, –2)

• (–6, –1)

• (6, 1)

• (12, 2)

Multiple Choice

Change the following equation to standard form

x²+y²-4x+12y-8=0. #34

• (x-2)²+(y-6)²=48

• (x-2)²+(y+6)²=48

• (x-6)²+(y-2)²=48

• (x+2)²+(y-6)²=48