To find:check whether the given
Answer to Problem 37PPE
The given triangle PQR is not a right angled triangle.
Explanation of Solution
Given info:
Consider the triangle PQR is a right angled triangle.
The vertices of PQR is denoted by
Consider the vertices of P
Consider the vertices of Q
Consider the vertices of R
Formula used:
Show the point−slope formula to find slope
If any two lines of the triangle don’t have the same slope value and also the slope value is a negative reciprocal of another line, then the triangle is said to be right angles-triangle.
The product of the two slopes of the lines of the triangle is -1, then the triangle is said to be right angles-triangle that is
Calculation:
Find the slope of the points P
Hence, the slope of the line PR is
Find the slope of the points R
Hence, the slope of the line RQ is
Find the slope of the pointsQ
Hence, the slope of the line QP is
Find whether the line PR and RQ is perpendicular to each other.
Hence, the line PR and RQ are not perpendicular to each other because it doesn’t satisfies the condition.
Find whether the line RQ and QP is perpendicular to each other.
Hence, the line RQ and QP are not perpendicular to each other because it doesn’t satisfies the condition.
Hence, the given triangle PQR is not a right angle triangle.
Conclusion:
Thus, the given triangle PQR is not a right angle triangle.
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