The rule (x + 2/3, y - 3/4)is applied to a polygon. find the coordinates of the point on the image that corresponds to each of these points on the original polygon.
To find the coordinates of the points on the image that correspond to each point on the original polygon, we will apply the given rule (x + 2/3, y - 3/4) to each individual point. Let's go step-by-step:
1. Take the coordinates of the original point.
2. Add 2/3 to the x-coordinate.
3. Subtract 3/4 from the y-coordinate.
4. The resulting coordinates are the coordinates of the image point.
Let's apply this rule to each point on the original polygon:
Original point: P(x, y)
Image point: Q(x', y')
1. P1(2, 4):
x' = 2 + 2/3 = 8/3 ≈ 2.67
y' = 4 - 3/4 = 13/4 ≈ 3.25
Q1(8/3, 13/4) ≈ (2.67, 3.25)
2. P2(-1, -3):
x' = -1 + 2/3 = -1/3 ≈ -0.33
y' = -3 - 3/4 = -15/4 ≈ -3.75
Q2(-1/3, -15/4) ≈ (-0.33, -3.75)
3. P3(5, -1):
x' = 5 + 2/3 = 17/3 ≈ 5.67
y' = -1 - 3/4 = -7/4 ≈ -1.75
Q3(17/3, -7/4) ≈ (5.67, -1.75)
Therefore, the coordinates of the image points corresponding to each point on the original polygon are:
Q1 ≈ (2.67, 3.25)
Q2 ≈ (-0.33, -3.75)
Q3 ≈ (5.67, -1.75)
To find the coordinates of the image point that corresponds to each of the points on the original polygon, we will apply the given rule to each point of the polygon.
Let's assume the original polygon has vertices (x1, y1), (x2, y2), (x3, y3), ..., (xn, yn).
To find the image point for each vertex, we will apply the rule (x + 2/3, y - 3/4) to each coordinate pair.
For example, to find the image point for the first vertex (x1, y1), you would add 2/3 to the x-coordinate and subtract 3/4 from the y-coordinate. Therefore, the corresponding image point would be ((x1 + 2/3), (y1 - 3/4)).
Repeat this process for each vertex to find the corresponding image points for the entire polygon.
a. (5 2/3, 2 1/4)
b. (5/6, 1/6)
c. (1 5/12, 1/20)