Coordinate Geometry and Graphs

Euler's formula for connected planar graphs states v - e + f = 2, where v is vertices, e is edges, and f is faces. Rearranging gives f = e - v + 2. This fundamental relationship applies to all connected planar graphs drawn without edge crossings.

Euler's formula for connected planar graphs states v - e + f = 2, where v is vertices, e is edges, and f is faces. Rearranging gives f = e - v + 2. This fundamental relationship applies to all connected planar graphs drawn without edge crossings.

Using the line equation (x-5)/(0-5) = (y-1)/(17/2-1) = (z-a)/(-13/2-a). For x=3: (3-5)/-5 = 2/5. Then (b-1)/(15/2) = 2/5 => b-1=3 => b=4. And (1-a)/(-13/2-a) = 2/5 => 5-5a = -13-2a => 18=3a => a=6.

 By the given condition, S and T are two different trees.  $\xi(S) = \xi(T)$ So, both S and T have the same number of vertices. Thus, |S| = |T|

Let the coordinates of the third vertex be (x,y). Applying the Pythagoras theorem in the right angled triangle, we get 8 = (x-2)² + y² + x² + (y-2)² 8 = x²+4-4x+y²+x²+y²+4-4y Cancelling 8, we get x²+y²-2x-2y=0 (Correct Answer)

Since ordered pair is written in the order (x, y), where x = x coordinate of that point and y = y coordinate of that point, so the ordered pair for point D is (11, –6). 

Because ordered pair representing any point is written as (x, y), where x = x-coordinate of that point and y = y-coordinate of that point. ^{_$\therefore$}    The ordered pair representing the point E is (11, 3).

The point B lies on y-axis; so the x-coordinate must be zero and y-coordinate must be 3. Thus, the ordered pair representing the point B is (0, 3).

 (–8, 7) represents point A on the graph.

The ordered pair representing C is (– 10, – 8) as the ordered pairs are written in the order (x, y), where x = x-coordinate of the point and y = y-coordinate of the point.

The ordered pair representing point H is (5, – 12) as ordered pairs are written in the order (x, y), where x = x-coordinate of the point and y = y-coordinate of the point.

As the ordered pair representing a point is written as (x, y), where x = x-coordinate of the point and y = y-coordinate of the point. Then, the ordered pair representing I is (3, 13).

As the ordered pair for any point is written in the form (x, y), where x = x co-ordinate of the point and y = y co-ordinate of the point. Then, the ordered pair representing F is given by (- 6, 10).

As the ordered pair representing any point is given by (x, y), where x = x co-ordinate of the point and y = y co-ordinate of the point. Then, the ordered pair representing J is given by (6, 6).