FIND MAGNITUDE AND DIRECTIONS OF TRANSLATIONS APPLIED ON A TRIANGLE. Question Linked below.

The three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

To find the magnitude and direction of the translations applied on a triangle, we need to know the coordinates of the vertices of the original triangle and the coordinates of the vertices of the transformed triangle.

Let's say the coordinates of the original triangle are (x1, y1), (x2, y2), and (x3, y3), and the coordinates of the transformed triangle are (x1', y1'), (x2', y2'), and (x3', y3').

The magnitude of the translation can be found by calculating the distance between the corresponding vertices of the original and transformed triangles using the distance formula. For example, the magnitude of the translation from (x1, y1) to (x1', y1') is given by:

sqrt((x1' - x1)^2 + (y1' - y1)^2)

Similarly, we can find the magnitudes of the other two translations.

The direction of the translation can be found by calculating the angle between the line connecting the corresponding vertices of the original and transformed triangles and the x-axis. We can use the arctangent function to find this angle. For example, the direction of the translation from (x1, y1) to (x1', y1') is given by:

tan^-1((y1' - y1)/(x1' - x1))

Similarly, we can find the directions of the other two translations.

Once we have the magnitudes and directions of the translations, we can describe the transformation using vector notation. The vector of the translation is given by:

< magnitude1, direction1 >

< magnitude2, direction2 >

< magnitude3, direction3 >

This represents the three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

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