Apply the rule (2x, 0.5y) to the vertices of triangle ABC to get triangle FGH.
Compare the corresponding measurements (side lengths, perimeter, area, angle measures) of the two triangles.
The x vertices will be 2 times as big as it was before, and the y vertices will be 0.5 times as big as before. hope this helps even tho i'm late!
To apply the rule (2x, 0.5y) to the vertices of triangle ABC, we need to multiply the x-coordinates of each vertex by 2 and the y-coordinates by 0.5. Let's begin by labeling the vertices of triangle ABC as A(x1, y1), B(x2, y2), and C(x3, y3).
1. Apply the rule to vertex A:
A' = (2x1, 0.5y1)
2. Apply the rule to vertex B:
B' = (2x2, 0.5y2)
3. Apply the rule to vertex C:
C' = (2x3, 0.5y3)
Now we have the vertices of triangle FGH as F(2x1, 0.5y1), G(2x2, 0.5y2), and H(2x3, 0.5y3).
To compare the corresponding measurements of the two triangles, let's examine each parameter:
1. Side lengths: Calculate the lengths of the sides of triangles ABC and FGH using the distance formula:
- For triangle ABC, calculate the lengths AB, BC, and AC.
- For triangle FGH, calculate the lengths FG, GH, and FH.
2. Perimeter: Add up the lengths of all sides of each triangle to obtain the perimeters of ABC and FGH.
3. Area: Calculate the area of each triangle using the formula for the area of a triangle:
- For triangle ABC, use the coordinates of its vertices to find the area.
- For triangle FGH, use the coordinates of its vertices to find the area.
4. Angle measures: Calculate the measures of the angles of both triangles using trigonometry or the Law of Cosines, based on the side lengths. You can use the inverse trigonometric functions to find the angles.
In summary, apply the rule (2x, 0.5y) to the vertices of triangle ABC to obtain triangle FGH. Then, compare the corresponding side lengths, perimeter, area, and angle measures of the two triangles using the distance formula, perimeter calculation, area formula, and trigonometric principles.