Soal Transformasi

The given statement explains that translasi is the movement or displacement of an object from one place to another due to a shift. This means that the statement is true.

The given statement is false. If the image of point B under a translation (6, -7) is B'(2, -3), then the coordinates of point B cannot be (-8, 4). The correct coordinates of point B can be found by subtracting the translation vector from the image coordinates, which gives (-4, -4).

The given statement states that the image of point A(-3,5) under the translation (3,-4) is A'(0,1). This means that when point A is translated 3 units to the right and 4 units down, it lands on point A'(0,1). Since the statement is true, it confirms that the translation has correctly moved point A to its new position at A'.

The statement is false because the point P(0, -5) would not be rotated to P'(-5, 0) by a rotation of 90 degrees about the origin. A rotation of 90 degrees about the origin would result in the point P being rotated to P'(5, 0) instead.

The statement is false because in reflection, the distance of the object to the mirror is equal to the distance of the image to the mirror, not the distance of the object to the image.

The given question is asking for the image of the point (-3, 3) under a rotation of 180 degrees about the origin. When a point is rotated 180 degrees about the origin, it is reflected across the x-axis and the y-axis. Therefore, the x-coordinate of the point (-3, 3) remains the same, but the y-coordinate changes sign. Thus, the image of the point (-3, 3) under the given rotation is (3, -3).

The point D(-2, 4) is dilated to D'(12, -24). To find the scale factor, we can compare the corresponding coordinates of D and D'. The x-coordinate of D' is 6 times the x-coordinate of D, and the y-coordinate of D' is -6 times the y-coordinate of D. Therefore, the scale factor is -6.

When a point P is reflected across the line y = 5, the y-coordinate remains the same while the x-coordinate changes sign. Since the y-coordinate of the reflected point P' is 3, it means that the y-coordinate of the original point P is also 3. The x-coordinate of P' is 1, so the x-coordinate of P must be -1. Therefore, the coordinates of point P are (-1, 3).

The point K(2, 6) is reflected across the line y = -x. To find the reflected point, we need to find the mirror image of K across the line. The line y = -x has a slope of -1, meaning it is a 45-degree line that passes through the origin. To reflect a point across this line, we can swap the x and y coordinates and change their signs. So, the reflected point of K(2, 6) would be (-6, -2).

The point M(0, -6) is translated by (8, 5), which means it is moved 8 units to the right and 5 units up. This results in the new coordinates of the point being (0+8, -6+5) = (8, -1).