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Neko [114]
3 years ago
15

A triangle ABC with vertices A(6,8) B(6,12) C(10,12) is rotated to 180. What are the coordinates of B

Mathematics
1 answer:
hichkok12 [17]3 years ago
8 0
Assuming rotation is about origin, then
R180:  (x,y)->(-x,-y)

So
A(6,8)->A'(-6,-8)
B(6,12)->B'(-6,-12)
C(10,12)->C'(-10,-12)
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First, let's convert each line to slope-intercept form to better see the slopes.

Isolate the y variable for each equation.

2x + 6y = -12

Subtract 2x from both sides.

6y = -12 - 2x

Divide both sides by 6.

y = -2 - 1/3x

Rearrange.

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Divide both sides by 2.

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Line c:

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Add 2y to both sides.

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Add 4 to both sides.

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Divide both sides by 2.

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Now, let's compare our new equations:

Line a: y = -1/3x - 2

Line b: y = 1.5x - 5

Line c: y = 1.5x + 2

Now, the rule for parallel and perpendicular lines is as follows:

For two lines to be parallel, they must have equal slopes.

For two lines to be perpendicular, one must have the negative reciprocal of the other.

In this case, line b and c are parallel, and they have the same slope, but different y-intercepts.

However, none of the lines are perpendicular, as -1/3x is not the negative reciprocal of 1.5x, or 3/2x.

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