Question

The coordinates of the points P, Q and R are given by (-2, 1), (1, 4) and (4, k) respectively. Find the value(s) of k if

Answer 1

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.

How to find the missing value of a coordinate

Herein we can find the value of the missing coordinate of point by the Pythagorean theorem, which is described below:

PQ = QR     (1)

$(Q_{x}-P_{x})^{2} + (Q_{y}-P_{y})^{2} = (R_{x}-Q_{x})^{2} + (R_{y}-Q_{y})^{2}$

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: brainly.com/question/26183488

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