apply the rule (1.5x, 1.5y) to the vertices of triangle ABC to get triangle PDR.
Compare the corresponding measurements (side lengths, perimeter, area, angle measures) of the two triangles.
The answer is ONE AND A HALF OF TRIANGLE ABC because the rule is you multiply the given number, which in this case is 1.5 for x and y.
To apply the rule (1.5x, 1.5y) to the vertices of triangle ABC, you need to multiply the coordinates of each vertex by the scaling factor of 1.5 in both the x and y directions.
Let's say the coordinates of the vertices of triangle ABC are:
A(x1, y1)
B(x2, y2)
C(x3, y3)
To get the coordinates of the vertices of triangle PDR, you need to multiply each coordinate by 1.5 in both the x and y directions:
D(1.5x1, 1.5y1)
P(1.5x2, 1.5y2)
R(1.5x3, 1.5y3)
Now, you can compare the corresponding measurements of the two triangles:
1. Side Lengths: To compare the side lengths, you can calculate the distance between each pair of vertices for both triangles. You can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Calculate the distances for each pair of vertices for both triangles (ABC and PDR). Compare the corresponding side lengths to see how they differ.
2. Perimeter: The perimeter of a triangle is the sum of its three side lengths. Calculate the perimeter for both triangles by adding up their corresponding side lengths. Compare the perimeters of the two triangles.
3. Area: The area of a triangle can be calculated using different methods, such as by using the formula 1/2 * base * height or by using Heron's formula. Calculate the area of both triangles using the same method and compare their areas.
4. Angle Measures: To compare the angle measures, you can calculate the angles formed by the sides of each triangle using trigonometry. You can use the arctan function to find the angle between two sides of a triangle.
Calculate the angles formed by the sides of both triangles for each corresponding vertex. Compare the angle measurements to see how they differ.
By comparing these measurements, you can understand the differences between triangle ABC and triangle PDR after applying the rule (1.5x, 1.5y).