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What is the reflection of the point (6, -3) in the line y = 2?
  • a)
    (-2, -3)
  • b)
    (6, 7)
  • c)
    (-6, 7)
  • d)
    (-2, 3)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is the reflection of the point (6, -3) in the line y = 2?a)(-2, -...
When a point is reflected about the x-axis, the x-coordinate remains the same and only the y-coordinate is transformed
∵ The line y = 2 is parallel to the x-axis, x-coordinate will remain the same after reflection
Now, along the y-direction, the distance between the reflected point and the line will be equal to the distance between the original point and the line
⇒ Distance between point and line along y-direction = |-3 – (2)| = |-5| = 5 unit
⇒ Y-coordinate of reflection = 2 + 5 = 7
∴ The reflection point is (6, 7)
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Most Upvoted Answer
What is the reflection of the point (6, -3) in the line y = 2?a)(-2, -...
When a point is reflected about the x-axis, the x-coordinate remains the same and only the y-coordinate is transformed
∵ The line y = 2 is parallel to the x-axis, x-coordinate will remain the same after reflection
Now, along the y-direction, the distance between the reflected point and the line will be equal to the distance between the original point and the line
⇒ Distance between point and line along y-direction = |-3 – (2)| = |-5| = 5 unit
⇒ Y-coordinate of reflection = 2 + 5 = 7
∴ The reflection point is (6, 7)
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Community Answer
What is the reflection of the point (6, -3) in the line y = 2?a)(-2, -...
Reflection of a point in a line:
When a point is reflected in a line, the reflected point lies on the other side of the line, maintaining the same distance from the line as the original point.

Given:
Point P(6, -3) and the line y = 2.

Steps to find the reflection:
To find the reflection of point P(6, -3) in the line y = 2, we can follow these steps:
1. Find the equation of the line perpendicular to y = 2 passing through point P.
2. Find the intersection point of the two lines.
3. Calculate the distance between the intersection point and the line y = 2.
4. Reflect the point P across the line y = 2 to find the reflected point.

Finding the equation of the perpendicular line:
The given line y = 2 has a slope of 0, so the perpendicular line will have an undefined slope. The equation of the perpendicular line passing through point P(6, -3) can be found as follows:
1. The slope of the perpendicular line is -1/0, which is undefined.
2. Using the point-slope form, the equation of the perpendicular line is x = 6.

Finding the intersection point:
To find the intersection point of the lines y = 2 and x = 6, we substitute the value of x from the equation of the perpendicular line into the equation of the given line:
x = 6, y = 2
The intersection point is (6, 2).

Calculating the distance:
To calculate the distance between the intersection point (6, 2) and the line y = 2, we can use the formula for the distance between a point and a line:
Distance = |ax + by + c| / sqrt(a^2 + b^2)
In this case, the equation of the line is y = 2, which can be rewritten as 0x + 1y - 2 = 0.
Using the formula, we get:
Distance = |0(6) + 1(2) - 2| / sqrt(0^2 + 1^2)
Distance = |0 + 2 - 2| / sqrt(1)
Distance = 0

Reflecting the point:
Since the distance between the intersection point (6, 2) and the line y = 2 is 0, it means that the point is already on the line. Therefore, the reflection of point P(6, -3) in the line y = 2 is the point itself, which is (6, -3).

Hence, the correct answer is option B) (6, -3).
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What is the reflection of the point (6, -3) in the line y = 2?a)(-2, -3)b)(6, 7)c)(-6, 7)d)(-2, 3)Correct answer is option 'B'. Can you explain this answer?
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