There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
Herein we can find the value of the missing coordinate of point by the Pythagorean theorem, which is described below:
PQ = QR (1)
[tex](Q_{x}-P_{x})^{2} + (Q_{y}-P_{y})^{2} = (R_{x}-Q_{x})^{2} + (R_{y}-Q_{y})^{2}[/tex]
If we know that P(x, y) = (- 2, 1), Q(x, y) = (1, 4) and R(x, y) = (4, k), then the missing value of the point R is:
[1 - (- 2)]² + (4 - 1)² = (4 - 1)² + (k - 4)²
(k - 4)² = 9
k - 4 = ± 3
k = 4 ± 3
There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
To learn more on Pythagorean theorem: https://brainly.com/question/26183488
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