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erastova [34]
3 years ago
13

Find the coordinates of B' after a reflection across the x-axis. show your work​

Mathematics
1 answer:
bazaltina [42]3 years ago
8 0

Answer:

  • B'(8, 6)

Step-by-step explanation:

Coordinates of point B = (8, -6)

<u>Reflection across the x-axis results in:</u>

  • (x, y) → (x, -y)

<u>Coordinates of B'</u>

  • (8, -6) → (8, -(-6)) = (8, 6)
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Any point, <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> on the parabola satisfies the definition of parabola, so there are two distances to calculate:

<span>Distance between the point on the parabola to the focusDistance between the point on the parabola to the directrix</span>

To find the equation of the parabola, equate these two expressions and solve for <span><span>y0</span><span>y0</span></span> .

Find the equation of the parabola in the example above.

Distance between the point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and <span><span>(<span>a,b</span>)</span><span>(<span>a,b</span>)</span></span> :

<span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span></span>

Distance between point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and the line <span><span>y=c</span><span>y=c</span></span> :

<span><span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span><span>| <span><span>y0</span>−c</span> |</span></span>

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Equate the two expressions.

<span><span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span>=<span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span></span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span>=<span>| <span><span>y0</span>−c</span> |</span></span></span>

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