Please help it’s for home work
1 answer:
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Answer:
-8
Step-by-step explanation:
Let's first establish the reference line (the one that the second line will be perpendicular to). We are told that this line passes through two points:
(1,1) and (-3,-1).
We'll find a line equation using the point slope form format to start:
(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.
(x,y) = (1,1)
(x1,y1) = (-3,-1)
Rearrange the equation:
(y - y1) = m * (x - x1)
m = (y - y1)/ (x - x1)
m = (1-(-1))/(1-(-3))
m = 2/4, or 1/2: The slope is 1/2. [<u>This is "m."]</u>
We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:
y = (1/2)x + b
Use either of the two given points. I'll use (1,1) since I have memorized the "1" math tables.
y = (1/2)x + b
1 = (1/2)(1) + b for (1,1)
b = 1/2
This makes the reference line: y = (1/2)x+(1/2)
===
The line perpendicular must have a slope that is the negative inverse of (1/2). This would be -(2/1), or -2.
We can then write y = -2x + b
To find be, enter the one given point for this line: (-3,-2)
y = -2x + b
-2 = -2(-3) + b
-2 = 6 + b
b = -8
The perpendicular line is thus:
y = -2x - 8
It has a y-intercept of -8
<u>Given</u>:
The line segments are AB, DB, AB, OB and BC
We need to determine the given line segments are radius, chord, diameter, secant or tangent of circle O.
<u>Line segment AB:</u>
A secant is a line segment that intersects the circle at two points.
Thus, the line segment AB is a secant.
<u>Line segment DB (</u><u>):</u>
The diameter of the circle is line that passes through the center and touches the two ends of the circle.
Thus, from the figure, the line segment DB passes through the center and touches the two ends of the circle.
Hence, the line segment DB is the diameter.
<u>Line segment AB (</u><u>):</u>
The line joining any two points on the circle is called the chord of the circle.
Thus, from the figure, the line segment AB touches the two points on the circle.
Hence, the line segment is the chord of the circle.
<u>Line segment OB (</u><u>):</u>
The radius of the circle is any line from the center of the circle to any point on the circle.
Thus, from the figure, the line segment OB is a line from center of the circle to the point B on the circle.
Hence, the line segment is the radius of the circle.
<u>Line segment BC:</u>
A tangent is a point that touches the exterior point of the circle exactly one time.
Thus, from the figure, the line segment BC is a touches the circle exactly once.
Hence, the line segment BC is the tangent of the circle.