Transformation geometry proof: reflections

Show $_p*$_l*$_p*$_l*$_p*$_l*$_p is a reflection in a line parallel to line l note $_p is a reflection about the line p

Word problem (airports)

1998 airports are each connected in both directions to exactly three other airports. Any airport can be reached from any other airport by a sequence of flights. It is decided to close down 200 of the airports, no two of which are connected by a single flight. Show that this can be done in such a way that any remaining airport ca ...continues

Transformation geometry proof: reflection

$_n$_m((x,y))= (x+6,y-3). Find equations for lines m and n. note: $_a is a reflection about line a

Tangency of three circles Tangency of 3rd circle to other circles

Tangency of three circles B elow is how I created the sketch shown in the other attachment: 1. Create two tangent circles with centers A and B. For convenience sake, let circle A hav ...continues

Lines through non-collinear points

Given three points, there is one line that can be drawn through them if the points are collinear. If the three points are noncollinear,there are three lines that can be drawn through pairs of points. For three points, three is the greatest number of lines that can be drawn through pairs of points. Determine the greatest number o ...continues

angles and sides of polygons

Given the following measures of a vertex angle of a regular polygon, determine how many sides it has? a. 150 degrees b. 156 degrees c. 174 degrees d. 178 degrees

Geometric mean

Prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments into which the altitude partians the hypotenuse.

Circumferance/area of a circle

Information is given about a circle in the following table. Fill in the missing entries of the table, and show how you come up with the answer. r=radius, d=diameter,C= circumference,A=area. Give answers to two decimal places. r d C A 231.04(symbol is pie) ...continues

Using Pythagoras theorem to draw exact lengths on a square lattice.

Represent the following lengths on a square lattice. Show all your work. a. square root of 5 b. square root of 17 c. square root of 18 d. square root of 29

Geometry Central Conicoid (part 1) Equation of the Tangent Plane to the Central Conicoid

Problem 1 Find the equation of the tangent plane to the central conicoid x2 – 4y2 + 3z2 + 2 = 0 at the point (1,2,0). Problem 2 Find whether the plane 2x + 3y + 2z =3 touches the central conicoid 2x2 + 3y2 + z2 = 1 or not.