On a coordinate plane, the location of 3 points are: (0,,-4), and (-1,-5). where would the fourth point need to be located in order to form a parallelogram?

(-6, 5)

Step-by-step explanation:

The slope of the segment from (0, 6) to (5, -4) is

m = (6--4)/(0-5) = (6+4)/(-5) = 10/(-5) = -2

The slope of the segment from (-1, -5) to (5, -4) is

m = (-5--4)/(-1-5) = (-5+4)/(-6) = (-1)/(-6) = 1/6

In order to be a parallelogram, the slopes of opposite sides must be the same.  This means the slope of the segment across from the segment with a slope of 1/6 must also have a slope of 1/6.

Working from (0, 6), to find the point with a slope of 1/6 we will work backward; going down 1 and back 6, we have (0-6, 6-1) = (-6, 5).

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1