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irga5000 [103]
3 years ago
6

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=?

Mathematics
2 answers:
Allisa [31]3 years ago
5 0

Answer:

y = x+5

Step-by-step explanation:

UNO [17]3 years ago
4 0

Answer:

  y = x+5

Step-by-step explanation:

A graph can help.

__

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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Find the value of r in (4,r),(r2) so that the slope of the line containing them is -5/3 A.-1/7 B-7. C 1/7 D. 7
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Answer:

Option D (7).

Step-by-step explanation:

The formula for gradient of the straight line is given by:

m = (y2 - y1)/(x2 - x1); where (x1, y1) and (x2, y2) are two fixed points on the straight line. It is given that (x1, y1) = (4, r) and (x2, y2) = (r, 2). The gradient of the straight line is given by -5/3. To find the value of r, simply substitute all the values in the gradient equation. Therefore:

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Cross Multiplying:

-5*(r - 4) = 3*(2 - r).

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r = 7.

Therefore, Option D is the correct answer!!!

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