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Sequences And Series

Question
CBSEENMA11015021
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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

Solution

Here, A ((3, -5, 7)) and B (-1, 7, -6) be the given vertices of a <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 C be (x, y, z)
rightwards double arrow Centroid of triangle ABC is straight G open parentheses fraction numerator 3 plus left parenthesis negative 1 right parenthesis plus straight x over denominator 3 end fraction comma space fraction numerator left parenthesis negative 5 right parenthesis plus 7 plus straight y over denominator 3 end fraction comma space fraction numerator 7 plus left parenthesis negative 6 right parenthesis plus straight z over denominator 3 end fraction close parentheses space left right arrow space left parenthesis 1 comma space 1 comma space 1 right parenthesis (Given)
rightwards double arrow          fraction numerator straight x plus 2 over denominator 3 end fraction equals 1 space or space straight x space equals space 1
               fraction numerator straight y plus 2 over denominator 3 end fraction equals 1 space or space straight y space equals space 1
                fraction numerator straight z plus 1 over denominator 3 end fraction equals 1 space or space straight z space equals space 2
Hence, vertex C is (1, 1, 2).
                 

Some More Questions From Sequences and Series Chapter

The coordinates of points in the XY-plane are of the form __________.

Coordinate planes divide the space into _______ octants.

Let P (-2, 3, -4) is a point in space. Find the co-ordinates of the foot of perpendicular from this point to ZX-plane.

Let P (-2, 3, -4) is a point in space. Find the foot of perpendicular from this point to the z-axis.

Let P (-2, 3, -4) is a point in space. Find the the perpendicular distance of P from XY-plane.

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

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