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

Summary

This video tutorial covers the core concepts of geometric transformations: translation, reflection, rotation, and dilation. Each transformation is explained step-by-step with practical examples. The video provides clear formulas for translating points and lines, reflecting over specific axes, rotating around the origin, and dilating points using a scale factor. By working through examples like translating point A(8, 3) by (-1, 5), reflecting point A(4, 2) over y=x, rotating point A(3, -4) by 90 degrees, and dilating point A(-4, 2) with a factor of -3, the video ensures learners can easily apply these transformations to various problems.

Takeaways

• 😀 The video covers the topic of geometric transformations, including translation, reflection, rotation, and dilation.
• 😀 The first topic discussed is translation, where the formula for translating a point (x, y) by (a, b) is x' = x + a and y' = y + b.
• 😀 In translation, the first example shows how to find the image of the point (8, 3) after translation by T = (-1, 5), resulting in (7, 8).
• 😀 The second translation example explains how to find the image of a line under translation. A line with the equation x + 2y = 5 is translated by T = (2, -3), resulting in the new equation x' + 2y' = 1.
• 😀 The next topic is reflection, starting with a reflection of the point (4, 2) over the line y = x. The reflection swaps the coordinates, resulting in the point (2, 4).
• 😀 Another reflection example involves reflecting a line 2x + 2y = 5 over the line y = -x. This leads to the equation -2x' - 2y' = 5.
• 😀 The next topic is rotation, where the formula for rotating a point (x, y) by 90 degrees counterclockwise around the origin is x' = -y and y' = x.
• 😀 A rotation example involves rotating the point (3, -4) 90 degrees counterclockwise around the origin, resulting in the new point (4, 3).
• 😀 The video then discusses rotation of a line. A line x + 3y = 5 is rotated 90 degrees counterclockwise, resulting in the equation -3x' + y' = 5.
• 😀 The final topic is dilation, where a point (x, y) is dilated by a scale factor k, with the new point being (k*x, k*y). An example shows dilating the point (-4, 2) by a scale factor of -3, resulting in the point (12, -6).

Q & A

What is the formula for translation in geometry?

The formula for translation 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 find the image of a point under translation?

To find the image of a point under translation, substitute the coordinates of the original point and the translation values into the formula x' = x + a and y' = y + b.

What is the result of translating point A(8, 3) by T(-1, 5)?

The result of translating point A(8, 3) by T(-1, 5) is point A'(7, 8).

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

To find the image of a line under translation, substitute the translation values into the equation of the line, adjust the variables as per the translation formula, and solve the new equation.

What is the formula for reflection of a point across the line y = x?

The formula for reflection of a point (x, y) across the line y = x is the image (y, x).

How do you find the image of a line under reflection across the line y = -x?

To find the image of a line under reflection across y = -x, switch the coordinates of the line’s equation, negate the x and y variables, and simplify to get the reflected line equation.

What is the image of point A(4, 2) when reflected across the line y = x?

The image of point A(4, 2) when reflected across y = x is point A'(2, 4).

How do you rotate a point 90 degrees counterclockwise around the origin?

To rotate a point 90 degrees counterclockwise around the origin, the new coordinates become (-y, x) where (x, y) are the original coordinates.

What is the image of point A(3, -4) after a 90-degree rotation around the origin?

The image of point A(3, -4) after a 90-degree rotation around the origin is point A'(4, 3).

How do you dilate a point with respect to the origin by a scale factor?

To dilate a point with respect to the origin by a scale factor k, multiply the original coordinates (x, y) by k to get the new coordinates (kx, ky).

What is the image of point A(-4, 2) when dilated by a scale factor of -3?

The image of point A(-4, 2) when dilated by a scale factor of -3 is point A'(12, -6).

How do you find the image of a line under dilation with a given scale factor?

To find the image of a line under dilation, multiply the x and y coordinates of each point on the line by the scale factor k, and adjust the equation of the line accordingly.

What is the equation of the line y = 2x - 1 after dilation by a factor of 3?

After dilation by a factor of 3, the equation of the line y = 2x - 1 becomes y' = 2x' - 3.