The coordinates of the endpoints of CE are C(-3, -7) and E(7,-2). Point M(3,-4) is in CE. What is the ratio of CM:ME

3:2

Step-by-step explanation:

The ratio of CM to ME is the ratio of lengths of the two segments.  Segment length is the square root of the sum of the squares of the differences of each coordinate direction.  For CM the difference of the x direction is

( -3-(+6) or -6 and the y direction (-7-(-4)) or 3.  Squaring each: -6^2 = 36 and 3^2 = 9.  The sum is 45 and the square root of 45 is 3 (5) ^1/2 by removal of the perfect squares.  For ME the x direction is 3 - (+7) = -4 and for the y direction is -4 - (-2) = 2.  Squaring each is -4^2 = 16 and 2^2 = 4. The sum is 20. The square rot of 20 is 2 (5) ^1/2.  The ratio is 3 (5)^ 1/2 : 2 (5) ^1/2 .  Since the square root of five is in both parts it can be removed.  Thus the ratio becomes 3 : 2.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: