Question

Example 3: TranslationA triangle with vertices A (-2, 1), B (2,4), and C(1, 1) is translated 3 units to theright and 5 units down.a.) Find the coordinates of the vertices of the image.b.) Graph triangle ABC and its image A'B'C'.

Answer 1

a) The vertices of the triangle after the transformation is

A' (1, -4)

B' (5, -1)

C' (4, -4)

b)

Step-by-step explanation

When a coordinate A(x, y) is translated horizontally along the x-axis by a units, the new coordinates, A'(x', y') is represented as

A[(x + a), y] when the translation is by a units to the right.

A[(x - a), y] when the translation is by a units to the left.

When a coordinate A(x, y) is translated vertically along the y-axis by b units, the new coordinates, A'(x', y') is represented as

A' [x, (y + b)] when the translation is by b units upwards.

A [x, (y - b)] when the translation is by b units downwards.

So, a movement of the cordinates of the triangle 3 units to the right and 5 units down will add 3 units to the x-coordinate and subtract 5 units from the y-coordinates

A (-2, 1) = A' [(-2 + 3), (1 - 5)] = A' (1, -4)

B (2, 4) = B' [(2 + 3), (4 - 5)] = B' (5, -1)

C (1, 1) = C' [(1 + 3), (1 - 5)] = C' (4, -4)

b) To graph the two triangles, we just plot the coordinates of the vertices and connect them. This is presented under 'Answer' above.

Hope this Helps!!!