Question

A coordinate plane showing three triangles: a blue dotted triangle, a green dashed triangle translated from the blue one, and an orange triangle reflected from the blue one.What two transformations are shown to demonstrate that the triangles are congruent?(2 points) degrees counterclockwise and (, )​​​​​​​Remaining Attempts : 3Skip to navigation

Answer 1

I can’t see the diagram you’re referring to. Could you either upload the image or give the coordinates of one pair of corresponding vertices (for example: blue vertex A = (x1,y1), green vertex A' = (x2,y2) and orange vertex A'' = (x3,y3))?

How I’ll find the two answers once you give that:

- Translation vector (for blue → green): subtract coordinates: (x2 − x1, y2 − y1). That gives the ( , ) vector you need.

- Rotation angle counterclockwise (for blue → orange): pick one corresponding vertex pair (x1,y1) → (x3,y3). If the rotation is about the origin, check if (x3,y3) equals one of these common 90°/180°/270° CCW images:
- 90° CCW: (x,y) → (−y, x)
- 180°: (x,y) → (−x, −y)
- 270° CCW: (x,y) → (y, −x)
If it’s not one of those, compute the angle between the vectors using the dot product formula:
angle = arccos( (v·w) / (|v||w|) )
and determine whether the rotation is CCW by checking the sign of the cross product (x1*y3 − y1*x3).

Send the image or coordinates and I’ll compute the exact degree and the translation vector.