△ABC is mapped to △A′B′C′ using each of the given rules.
Which rules would result in △ABC being congruent to or not congruent to △A′B′C′ ?
Drag and drop each rule into the boxes to classify it as Congruent or Not Congruent.
(x,y) → (5x, 5y)
(x,y) →(x, - y)
(x, y) → (x + 5, y)
(x, y) → ( 0.5x, 0.5y)
(x, y) → (-x, -y)
To determine whether △ABC is congruent to △A′B′C′ using the given rules, we need to analyze each rule and consider its effect on the corresponding vertices of the triangles. Here's how you can approach this problem:
1. (x,y) → (5x, 5y):
This rule scales the coordinates of each vertex by a factor of 5. Since the scale factor is the same for both the x and y coordinates, this rule results in congruent triangles. Therefore, drag and drop this rule into the "Congruent" box.
2. (x,y) → (x, -y):
This rule reflects the vertices of the triangle across the x-axis, changing the sign of the y-coordinate. This transformation does not preserve the shape and size of the triangle, so △ABC and △A′B′C′ are not congruent. Drag and drop this rule into the "Not Congruent" box.
3. (x, y) → (x + 5, y):
This rule shifts the vertices of the triangle horizontally by 5 units to the right. Although the position of the triangles may change, this transformation does not alter the shape or size. Thus, △ABC and △A′B′C′ remain congruent. Drag and drop this rule into the "Congruent" box.
4. (x, y) → (0.5x, 0.5y):
This rule scales the coordinates of each vertex by a factor of 0.5. Since the scale factor is the same for both the x and y coordinates, this rule results in congruent triangles. Therefore, drag and drop this rule into the "Congruent" box.
5. (x, y) → (-x, -y):
This rule reflects the vertices of the triangle across the origin, changing the sign of both the x and y coordinates. Similar to rule 2, this transformation does not preserve the shape and size of the triangle, so △ABC and △A′B′C′ are not congruent. Drag and drop this rule into the "Not Congruent" box.
By following these steps and analyzing the effect of each rule, you can correctly classify whether the triangles are congruent or not congruent.
Congruent:
1) (x, y) → (-x, -y)
2) (x, y) → (x, -y)
Not Congruent:
1) (x,y) → (5x, 5y)
2) (x, y) → (x + 5, y)
3) (x, y) → (0.5x, 0.5y)
translations, rotations and reflections do not change size
the x and y scales must both 1 or -1
If x and y are scaled equally (but not 1) then the triangles will be similar but not congruent.