Find the co-ordinates of the centroid of triangle whose vertices

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

Advertisement

81. Find the co-ordinates of the centroid of triangle whose vertices are A (2, 3, -1), B (1, 3, -2) and C (3, 0, 3).


straight A space left parenthesis 2 comma space 3 comma space minus 1 right parenthesis space left right arrow space left parenthesis straight x subscript 1 comma space straight y subscript 1 comma space straight z subscript 1 right parenthesis

<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>

Let centroid be G (x, y, z)

rightwards double arrow                           space space space space space space straight x equals fraction numerator straight x subscript 1 plus straight x subscript 2 plus straight x subscript 3 over denominator 3 end fraction equals fraction numerator 2 plus 1 plus 3 over denominator 3 end fraction equals 2

                                      space space straight y equals fraction numerator straight y subscript 1 plus straight y subscript 2 plus straight y subscript 3 over denominator 3 end fraction equals fraction numerator 3 plus 3 plus 0 over denominator 3 end fraction equals 2
 
                                        straight z equals fraction numerator straight z subscript 1 plus straight z subscript 2 plus straight z subscript 3 over denominator 3 end fraction equals fraction numerator left parenthesis negative 1 right parenthesis plus left parenthesis negative 2 right parenthesis plus 3 over denominator 3 end fraction equals 0
Hence, the centroid is G (2, 2, 0).
124 Views

Advertisement
82. The centroid of a triangle ABC is at the point (1, 1, 1). If the co-ordinates of A and B are (3, -5, 7) and (-1, 7, -6) respectively, find the co-ordinates of the point C
138 Views

83. If the origin is the centroid of triangle PQR, with vertices P(2a, 2, 6), Q(- 4, 3b, - 10) and R(8, 14, 2c). Find the values of a, b and c. 
139 Views

84. Without using distance formula, show that A (-1, 2, 1), B (1, -2, 5) C (4, - 7, 8) and D (2, - 3, 4) are the vertices of a parallelogram ABCD. 
100 Views

Advertisement
85. Three vertices of a parallelogram ABCD are A (3, -1, 2), B (1, 2, -4), and C (-1, 1, 2). Find the co-ordinates of the fourth vertex.
147 Views

 Multiple Choice QuestionsLong Answer Type

86. The co-ordinates of the mid-points of sides BC, CA and AB of ∆ ABC are (2, 1, -1), (3, 2, 4) and (1, -2, 3) respectively. Find the co-ordinates of vertices A, B and C.
120 Views

 Multiple Choice QuestionsShort Answer Type

87. Find the co-ordinates of a point P which divides the join of A (1, - 2, -1) and (1, 5, -8) internally in ratio 3 : 4.
89 Views

88. Find the co-ordinates of a point which divides the line joining points A (2, - 1, 3) and B (1, 4, 2) externally in ratio 2 : 3.
91 Views

Advertisement
89. Find the ratio in which the line joining points A (2, 4, - 3) and B (-3, 5, 2) is divided to XY-plane.
114 Views

90. Find the ratio in which the line joining points P (-3, 4, 5) and Q (5, 1, -1) divided by YZ-plane.
112 Views

Advertisement