Expressing Geometric Properties with Equations

Directions: Using the integers -9 to 9 at most one time fill in the boxes to create a right triangle on the coordinate plane. Source: Tracy Conte

Directions: Using the integers -9 to 9, at most one time each, fill in the boxes to create a circle and a point on the circle. Source: Robert Kaplinsky

Directions: Using the integers -9 to 9, at most one time each, fill in the boxes to create a circle and a point on the circle with the point being as close to the origin as possible. Source: Robert Kaplinsky

Directions: Using the integers -9 to 9 at most one time each, fill in the boxes to create coordinates that represent the vertices of the triangle with the smallest possible area. Source: Robert Kaplinsky

Directions: Using the integers -9 to 9 at most one time each, fill in the boxes to create coordinates that represent the vertices of two triangles: one with an area of less than 55 units2 and one with an area of more than 55 units2. You may reuse all the integers each time. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create two perpendicular lines whose solution is as close to the origin as possible. Source: Robert Kaplinsky

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create two perpendicular lines. Source: Robert Kaplinsky

Directions: Using the integers -9 to 9 at most one time each, place a digit in each box to create endpoints for two different line segments whose midpoint is (1, 3). One line segment should have a positive slope and the other should have a negative slope. You may reuse all the integers for each line segment. Source: Robert Kaplinsky …

Directions: Using the integers -9 to 9 at most one time each, place a digit in each box to create endpoints for the longest possible line segment whose midpoint is (1, 3). Source: Robert Kaplinsky in Open Middle Math

Directions: Use the digits 0 to 9, at most one time each, to fill in ordered pairs for all three points, such that the area of Triangle ABC is closest to 6 square units. A ( ___, ___ ) B ( ___, ___ ) C ( ___, ___ ) Source: Henry Wadsworth