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- To find a reflection about a point, Find the coordinates of the point of reflection. Translate the point of reflection as well as the object such that the point of reflection is mapped to the origin. For example, given the point of reflection (-1, 3), move the point (as well as the object) 1 unit to the right and 3 units down.
People also ask
What is a reflection on the coordinate plane?
How do you find the coordinates of a point of reflection?
How do you find a line of reflection?
What is a point reflection?
In standard reflections, we reflect over a line, like the y-axis or the x-axis. For a point reflection, we actually reflect over a specific point, usually that point is the origin . Formula r(origin) (a, b) → (−a, −b) Formula r ( o r i g i n) ( a, b) → ( − a, − b) Example 1.
The formula for finding the foot of the perpendicular from a point $(x_1,y_1)$ to the line $ax+by+c=0$ is given by: $$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{-(ax_1+by_1+c)}{a^2+b^2}$$ For finding the image of the point in the same line, we just multiply the rightmost term by 2.
The closest point on the line should then be the midpoint of the point and its reflection. To do this for y = 3, your x-coordinate will stay the same for both points. The y-coordinate will be the midpoint, which is the average of the y-coordinates of our point and its reflection. (y1 + y2) / 2 = 3 y1 + y2 = 6 y2 = 6 - y1
- 4 min
- Sal Khan
One thing you could do is this: Consider the point given and the line of reflection (which is oblique). Now, draw a line from the point till you intersect the line of reflection. After you intersect it, draw a line perpendicular to the line you just drew, but make sure that this line is equal in length to the first line.
- 2 min
Transcript. We can plot points after reflecting them across a line, like the x-axis or y-axis. Reflections create mirror images of points, keeping the same distance from the line. When we reflect across the y-axis, the image point is the same height, but has the opposite position from left to right. Questions.
- 4 min
A reflection across the line y = x switches the x and y-coordinates of all the points in a figure such that (x, y) becomes (y, x). Triangle ABC is reflected across the line y = x to form triangle DEF. Triangle ABC has vertices A (-2, 2), B (-6, 5) and C (-3, 6). Triangle DEF has vertices D (2, -2), E (5, -6), and F (6, -3).
Answer. Recall that, for a general point 𝑃 ( 𝑥, 𝑦), a reflection in the 𝑥 - a x i s maps 𝑃 ( 𝑥, 𝑦) → 𝑃 ′ ( 𝑥, − 𝑦). The effect is that the position of 𝑃 ′ will mirror that of 𝑃, on the opposite side of the 𝑥 - a x i s and at the same perpendicular distance from the 𝑥 - a x i s as 𝑃.
