Question 81

Denote the origin by O , (2, 1) by P and (-1, 2) by Q. If R and S are marked on the XY -plane such that OR = 30 units, OS = 40 units. P lies on OR and Q on OS , then what is the distance between R and S , in the given unit?

Name: Denote the origin by O , (2, 1) by P and (-1, 2) by Q. If R and S are marked on the XY -plane such that OR = 30 units, OS = 40 units. P lies on OR and Q on OS , then what is the distance between R and S , in the given unit?
Uploaded: 2026-06-14T11:35:28.980930+05:30
Duration: 6 min 43 s
Description: Denote the origin by O , (2, 1) by P and (-1, 2) by Q. If R and S are marked on the XY -plane such that OR = 30 units, OS = 40 units. P lies on OR and Q on OS , then what is the distance between R and S , in the given unit?

Solution

Join the points O and P, the slope of this line is 1/2/ Join the points O and Q, the slope of this line is -2. The product of slopes of two perpendicular lines will be -1. These two lines are perpendicular. The point R lies on OP and S on OQ. Since these two lines are perpendicular, the line joining R and S will be the hypotenuse. So it is $$\sqrt{\ 30^2+40^2}=50$$.

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