Question
In triangle PQR, the equation of side PQ is y = x. The equation of side QR is y = -x. Determine whether
triangle is a right triangle
Hint:
The equations of sides are given ,check whether the angle between those lines is 90(degrees)or not .
The correct answer is: Yes, The triangle is a right angle triangle with right angle at Q
ANS :-. Yes, The triangle is a right angle triangle with right angle at Q .
Explanation :-
Step 1:- Find the slopes of the given side from using given equations.
PQ side has y = x as equation comparing it with y = mx
We get slope of PQ (m1) = 1
QR side has y = - x as equation comparing it with y = mx
We get slope of QR (m2) = -1
Step 2:- check for perpendicular condition between sides
IF m1 × m2 = -1 we get the sides are perpendicular
m1 × m2 = 1 × -1 = -1
we get both the PQ perpendicular to QR .so, angle Q = 90 (degrees)
IF any angle in triangle PQR is 90° then triangle PQR is a right angle triangle
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Instead of adding 2 on both sides, we can also understand the concept by taking -2 of the right hand side on the left hand side and then the sign changes to + 2 . Similarly, instead of subtracting both sides by , we can understand it by saying that we take + x from the left hand side to the right hand side, and here it becomes - x .
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
