Don L. answered 01/30/17
Tutor
5
(18)
Fifteen years teaching and tutoring basic math skills and algebra
Hi Aaron, to find the center of the circle, you need several steps.
Step 1: You need to find the two lines that are perpendicular to the two given lines.
For a line to be perpendicular to a given line, the slope will be the negative reciprocal of the slope of the given line.
For line: x - 2y + 16 = 0, the slope of a line in standard form is -A/B. Here B is -2 and A is 1. The Slope of the given line is 1/2, therefore, the slope of the perpendicular line is -2.
For line: y = 2x - 1, the slope of a line in the slope-intercept form is the value associated with the x-term, or 2. The slope of the line perpendicular to the given line is -1/2.
We now have the slopes of the two lines perpendicular to the two given lines.
Step 2: Given the slopes of the two line that are perpendicular, you now need to find the two lines.
For the line that is perpendicular with a slope of -2, use the given point, (0, 8) and the point-slope form of the line to find the line.
y - y1 = m * (x - x1)
Substitute for x1, y1, and m:
y - 8 = -2 * (x - 0)
y - 8 = -2x
In standard form: 2x + y = 8
For the line that is perpendicular with a slope of -1/2, use the given point, (3, 5) and the point-slope form of the line to find the line.
y - y1 = m * (x - x1)
Substitute for x1, y1, and m:
y - y1 = m * (x - x1)
Substitute for x1, y1, and m:
y - 5 = (-1/2) * (x - 3)
y - 5 = -x/2 + 3/2
In standard form, with no fractions: x + 2y = 13
Step 3:
Solve the two perpendicular line equations as a system of equations for x and y:
x + 2y = 13
2x + y = 8
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The values you find for x and y are the ordered pair for the center of the circle.
I'll leave that up to you.
Questions?