Answer:
7x -2y = 6
Step-by-step explanation:
The perpendicular bisector has a slope that is the opposite of the reciprocal of the slope of the segment between the two points. It must go through the midpoint of the segment.
The latter can be found by averaging the coordinates of the end points:
((-5, 6) +(9, 2))/2 = ((-5+9)/2, (6+2)/2) = (2, 4)
The difference in endpoint coordinates is ...
(Δx, Δy) = (9-(-5), 2-6) = (14, -4)
For our purpose, we're only interested in the ratio of these values, so we can divide both by the common factor of 2:
(Δx, Δy) = (7, -2)
A line perpendicular to this segment through the point (h, k) can be written as ...
Δx·x +Δy·y = Δx·h +Δy·k
7x -2y = 7(2) -2(4)
7x -2y = 6 . . . . . . . standard form equation for the perpendicular bisector
Step-by-step explanation:
1. We we can split 4p into 9p - 5p, and now we have 3p² + 9p - 5p - 15 = 0. We can take out 3p from the first 2 terms and -5 from the last 2 terms. This gets us 3p (p + 3) -5 (p + 3) = 0. These two terms have (p + 3) as a common facor, so we can take that out as well, which give us (p + 3)(3p - 5) = ). Using Zero Product Property, p + 3 = 0 and 3p - 5 = 0, and when we solve each equation, we get p = -3, p= 5/3.
2. We will use the same process.
6x² + 14x - 3x - 7 = 0
2x (3x+7) - 1 (3x+7) = 0
(3x + 7)(2x - 1) = 0
3x + 7 = 0, 2x - 1 = 0
x = -7/3, x=1/2
Hope this helps!
Answer:
The ordered pair (-6, -1) is the only solution.
Step-by-step explanation:
-6x + y = 35
Let's plug in the points.
(-1, -7) --> -6(-1) - 7 = 6 - 7 = -1 which does not equal 35
(-6, -1) --> -6(-6) -1 = 35
(-1, -6) --> -6(-1) - 6 = 0 which does not equal 35
(-7, -1) --> -6(-7) - 1 = 41 which does not equal 35
