Given triangle ABC with coordinates A(−5, 4), B(−5, 1), and C(−7, 0), and its image A′B′C′ with A′(−1, 0), B′(−4, 0), and C′(−5,
−2), find the line of reflection.
The line of reflection is at y=?
The line of reflection is at y=?
2 answers:
Answer:
y = x+5
Step-by-step explanation:
A graph can help.
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The line of reflection will pass through the midpoints of AA' and BB'.
The midpoint of AA' is ((-5, 4) +(-1, 0))/2 = (-3, 2)
The midpoint of BB' is ((-5, 1) +(-4, 0))/2 = (-4.5, 0.5)
The slope of the line through these points is ...
Δy/Δx = (2 -0.5)/(-3-(-4.5)) = 1.5/1.5 = 1
Then the y-intercept can be found from
y = x + b
2 = -3 + b
5 = b
So, the line of reflection is ...
y = x + 5
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Answer:
<h2>For c = 5 → two solutions</h2><h2>For c = -10 → no solutions</h2>Step-by-step explanation:
We know
for any real value of <em>a</em>.
|a| = b > 0 - <em>two solutions: </em>a = b or a = -b
|a| = 0 - <em>one solution: a = 0</em>
|a| = b < 0 - <em>no solution</em>
<em />
|x + 6| - 4 = c
for c = 5:
|x + 6| - 4 = 5 <em>add 4 to both sides</em>
|x + 6| = 9 > 0 <em>TWO SOLUTIONS</em>
for c = -10
|x + 6| - 4 = -10 <em>add 4 to both sides</em>
|x + 6| = -6 < 0 <em>NO SOLUTIONS</em>
<em></em>
Calculate the solutions for c = 5:
|x + 6| = 9 ⇔ x + 6 = 9 or x + 6 = -9 <em>subtract 6 from both sides</em>
x = 3 or x = -15