Two perpendicular lines intersect on the y-axis. the equation of one line is 4y - x - 24 =0. determined the equation of the other line

y  + 4x - 6 = 0

Step-by-step explanation:

Rearranging the given equation:-

4y = x + 24

y = 1/4 x + 6  

This has a y intercept of  (0, 6) and a slope of 1/4.

Thus, the other line has a slope of -4 and  passes through the point (0,6) also.

Using the Point-slope form of a straight line:-

y - y1 = m(x - x1)

y - 6 = -4(x - 0)

y  + 4x - 6 = 0  is the required equation  

GH = 25 in

Step-by-step explanation:

Since the are similar quadrilaterals, their side lengths are in proportion to each other.

Look at the letter ordering, ABCD   and EFGH,   the represent corresponding points in the quadrilateral, so

AB and EF are the same corresponding side of the quadrilateral.  For the first quadrilateral, A is the first letter, B is the second. In the second quadrilateral, E is the first letter, and F is the second.  A corresponds to E, and B corresponds to F.  The rest of the letters correspond the same way

as are CD and GH

So we have a proportion, "30 is to 50 as 15 is to GH"

30/50 = 15/GH  

Solve for GH by cross-multiplying (here GH is one variable)

30GH = 750

   GH = 25