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Distance & Midpoint

100

This is the midpoint of the 2 points (3,7) and (14,-9).

What is (8.5,-1)? 

200

This is the midpoint of the 2 points (21,-100) and (-99,24). 

What is (-39,-38)?

300

Find the distance between (3,-8) and (-15,-9). 

What is sqrt(325)?

400

Find the distance between (121,-87) and (-41,29). 

What is sqrt(39,700)?

500

Give the generalized formulas for both midpoint and distance. 

MP: (X2+X1)/2, (Y2+Y1)/2

Distance: sqrt((x2-x1)^2+(y2-y1)^2)

Circles

100

What is the area of a circle with a diameter of 50?

What is 625pi?

200

What is the circumference and area of a circle with a radius of 8? 

Circumference: What is 16pi?

Area: What is 64pi?

300

Identify the center and radius of the following circle. 

(x+4)^2+(y-9)^2=38

Center: What is (-4,9)? 

Radius: What is sqrt(38)?

400

What is the equation of the circle in standard form based off the following: x^2+y^2+8x-6y-11=0?

What is (x+4)^2+(y-3)^2=36

500

What is the center and radius based off the following equation? 

x^2+y^2-4x+2y-4=0

Center: (2,-1)

Radius:3

Pythagoras

100

Pythagoras was terrified of this kind of food. 

What are beans? 

200

This is a set of points that satisfies the Pythagorean Theorem using only WHOLE numbers. 

What is a Pythagorean Triple?

300

These are the classic Pythagorean Triples. Looking for 2. 

What are (3,4,5) and (5,12,13)?

400

Does (20,21,29) satisfy the Pythagorean Theorem? 

Yes. 

500

Does (48,55,72) satisfy the Pythagorean Theorem? 

No. 

Border

100

A point (15,8) lies directly on the border of a circular orchard. What is the radius of this orchard? 

What is 17? 

200

Based off the fact that (15,8) lies on the border, list all other points that lie on the border that are ONLY POSITIVE. 

What are (8,15), (17,0) and (0,17)? 

300

Determine whether the point is within, on or outside the border. 

(15,9)

What is out? 

400

A horizontal distance is 45 and the length of the hypotenuse is 53. What is the vertical distance? 

What is 28? 

500

List all points that lie directly on the border of a circular orchard with a radius of 53. A point that lies on there is (28,45). 

What is (45,28), (53,0), (0,53), (-53,0), (0,-53), (45,-28), (28,-45), (-45,-28), (-28,-45), (-28,45) and (-45,28)? 

If-Then

100

If there is a right triangle, then...

Then the lengths of the right triangle satisfy the Pythagorean Theorem. 

200

If a point (x,y) satisfies the following the inequality, x^2+y^2 < r^2, then 

Then the point is within the border.

300

If a point lies on a perpendicular bisector, then...

Then the point is equidistant from any 2 given points. 

400

If a point (x,y) satisfies the following inequality, x^2+y^2=r^2, then...

Then the point lies directly on the border. 

500

If the lengths of the sides of a triangle satisfy the Pythagorean Theorem, then...

Then the triangle is a right triangle.