Let's first establish the coordinates of points T, P, and Z based on the given descriptions:
- Point T is 1 unit right and 4 units up from the origin (0,0). Hence, the coordinates of T are (1, 4).
- Point P is 6 units right and 2 units up from the origin (0,0). Hence, the coordinates of P are (6, 2).
- Point Z is 3 units right and 5 units up from the origin (0,0). Hence, the coordinates of Z are (3, 5).
Now, regarding your questions:
- The coordinates of Point Z are (3, 5).
- The coordinates of Point P are (6, 2).
- The point with coordinates (1, 4) is Point T since it's the only point that matches those coordinates.
- To find the coordinates of the fourth vertex of the rectangle that can be made from points T(1, 4), P(6, 2), and Z(3, 5), we can utilize the properties of rectangles.
The fourth vertex can be determined by considering the opposite corners of the rectangle formed. The coordinates can be derived as follows:
Given the points:
- T (1, 4)
- P (6, 2)
- Z (3, 5)
To find the fourth vertex (let's call it W), we can calculate it using the midpoints or diagonals:
- Calculate the diagonally opposite point:
- X = x1 + x2 + x3 - x4
- Y = y1 + y2 + y3 - y4
However, here for a rectangular shape: Let the coordinates of W be \( (x_W, y_W) \) then we can pair them such that:
- (x_T, y_T) and (x_W, y_W) must have the same x-coordinate or y-coordinate with point P and Z respectively.
An easy way to find the fourth point using the idea of the intersection means shifting the coordinates: For example: \( x_W = (1 + 6 + 3) - (26) = -4, \) \( y_W = (4 + 2 + 5) - (22) = 11. \)
However, rectangle properties give that if we take the average of points T and P, we can definitely derive the missing point. But in short with some trials that fit the matrix properties i.e.: So the likely fourth box point W = (3,2) or (6, 5)
Thus the fourth vertex coordinates can be adequately answered as potentially (6, 5).
In conclusion: 4. The coordinates for the fourth vertex are (0, 5) based on oppositions coordinates tweaks but also can be (1,2) based on diagonal interpretation.
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