A triangle from point P to Q is 3m and point Q to point R is 4m. What is the displacement to point P

To determine the displacement from point R to point P, we can use the concept of vector addition and the Law of Cosines or the Pythagorean theorem if we know the angle between the sides PQ and QR. However, based on your description, we can assume the points form a triangle where: - \(P\) is point P, - \(Q\) is point Q, - \(R\) is point R. Given: - The length of segment \(PQ = 3m\) - The length of segment \(QR = 4m\) ### Case 1: If PQ and QR are perpendicular If angle \(Q\) forms a right angle, you can apply the Pythagorean theorem: \[ PR = \sqrt{PQ^2 + QR^2} \] Substituting the given lengths: \[ PR = \sqrt{3^2 + 4^2} \] \[ PR = \sqrt{9 + 16} \] \[ PR = \sqrt{25} \] \[ PR = 5m \] ### Case 2: If angle Q is not a right angle Without further information about the angle \(Q\) (the angle between segments \(PQ\) and \(QR\)), we cannot determine a specific distance for \(PR\) using just the lengths. In summary, if \(PQ\) and \(QR\) are perpendicular, the displacement from point R to point P would be 5m. If the angle is different, further information would be needed to calculate the exact displacement.