Question 53 Section Formula Exercise 11 Next
Answer:
Solution: The centroid of a triangle is where the medians of the triangle cross. Unlike other points of concurrency in a triangle, the centroid always lies inside one. Let third vertex be C(x3,y3). Given (x1,y1) = (3,-5) (x2,y2) = (-7,4) Co-ordinates of centroid are (2,-1) Co-ordinates of the centroid of a triangle, whose vertices are (x1,y1), (x2,y2) and (x3,y3) are [(x1 + x2+ x3)/3, (y1 + y2+ y3)/3] (x1 + x2+ x3)/3 = (3+-7+x3)/3 = 2 [x co-ordinate of centroid] -4+x3 = 2×3 -4+x3 = 6 x3 = 6+4 x3 = 10 (y1 + y2+ y3)/3 = -1 [y co-ordinate of centroid] -5+4+y3 = -1×3 -1+y3 = -3 y3 = -3+1 y3 = -2 Hence the third vertex is (10,-2).
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Prev Article Next Article (Last Updated On: January 20, 2020) Problem Statement: ECE Board April 1999Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 square units, what is the locus of the third vertex? Problem Answer:The locus of the third vertex of a triangle is x – 4y = -10. Latest Problem Solving in Analytic Geometry Problems (Points, Lines and Circles)More Questions in: Analytic Geometry Problems (Points, Lines and Circles) Online Questions and Answers in Analytic Geometry Problems (Points, Lines and Circles)MCQ in Analytic Geometry Problems (Points, Lines and Circles) Prev Article Next Article |
Two vertices of a triangle are (2 4) and (-2 3)
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