(LENGKAP) TRANSFORMASI GEOMETRI - Translasi, Refleksi, Rotasi dan Dilatasi

Summary

This video provides an in-depth tutorial on geometric transformations, covering translation, reflection, rotation, and dilation. It explains the process of determining the image of a point or line after each transformation using specific formulas. The video includes step-by-step examples for each transformation type, such as translating a point, reflecting a point across lines, rotating points around the origin, and dilating points with a scale factor. The tutorial is designed to make these concepts easy to understand, helping viewers grasp the core principles of geometry in a clear and accessible way.

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Q & A

What is the general formula used for translation of points?

The general formula for translation of points is x' = x + a and y' = y + b, where (x, y) is the original point, and (a, b) are the translation values.

How do you apply translation to the point A(8, 3) using the translation T = (-1, 5)?

To apply the translation T = (-1, 5) to point A(8, 3), we use the formula x' = x + a and y' = y + b. Substituting values, x' = 8 + (-1) = 7, and y' = 3 + 5 = 8, so the translated point is A'(7, 8).

How do you find the image of a line after translation?

To find the image of a line after translation, you apply the translation formula to all points on the line. For example, the equation of the line x + 2y = 5 becomes x' + 2y' = 5 after applying a translation. The transformation changes the coordinates of all points on the line, yielding a new equation.

What is the effect of reflection over the line y = x on a point (x, y)?

Reflection over the line y = x swaps the coordinates of the point. Therefore, the image of the point (x, y) after reflection over y = x will be (y, x).

How do you reflect the point A(4, 2) over the line y = x?

To reflect the point A(4, 2) over the line y = x, swap the coordinates. The reflected point A' will be A'(2, 4).

How does reflection over the line y = -x affect the coordinates of a point?

Reflection over the line y = -x negates both coordinates and swaps them. Therefore, the image of a point (x, y) will be (-y, -x).

What happens to the equation of a line after reflection over y = -x?

After reflecting a line over y = -x, you replace x with -y and y with -x in the original equation. For example, the equation 2x + 2y = 5 becomes -2x' - 2y' = 5 after the reflection.

What is the general formula for rotation of a point (x, y) around the origin (0, 0) by 90 degrees?

The formula for rotating a point (x, y) around the origin by 90 degrees is (x', y') = (-y, x).

What is the result of rotating the point A(3, -4) by 90 degrees around the origin?

Rotating the point A(3, -4) by 90 degrees around the origin gives the image A'(4, 3).

How do you perform dilation of a point (x, y) with a scale factor k and center at the origin?

For dilation with a scale factor k and the center at the origin, the new coordinates (x', y') are found by multiplying the original coordinates (x, y) by the scale factor k. Thus, x' = k * x and y' = k * y.

What happens to the point A(-4, 2) when dilated by a factor of -3 with the center at the origin?

When the point A(-4, 2) is dilated by a factor of -3 with the center at the origin, the new coordinates are A' = (k * x, k * y). Substituting the values, A' = (-3 * -4, -3 * 2) = (12, -6).

How do you find the image of a line after dilation?

To find the image of a line after dilation, you apply the dilation formula to every point on the line. The equation of the line changes accordingly. For example, the line y = 2x - 1 will be dilated by a factor of 3, resulting in a new equation: y' = 2x' - 3.