{"id":277,"date":"2022-04-13T10:32:46","date_gmt":"2022-04-13T10:32:46","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=277"},"modified":"2025-03-01T06:54:50","modified_gmt":"2025-03-01T06:54:50","slug":"n-8-dilations-find-the-coordinates","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/n-8-dilations-find-the-coordinates\/","title":{"rendered":"N.8 Dilations: find the coordinates"},"content":{"rendered":"\n

Dilations: find the coordinates<\/h2>\n\n\n\n

A dilation enlarges or reduces a figure.<\/p>\n\n\n\n

Learn with an example<\/p>\n\n\n\n

\n
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Write the coordinates of the vertices after a dilation with a scale factor of 5, centred at the origin.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

The scale factor of a dilation is the ratio of a length in the image to the corresponding length in the original figure.<\/p>\n\n\n\n

This dilation is centred at the origin, so you can find the image by multiplying the x<\/em>– and y<\/em>-coordinates by the scale factor.<\/p>\n\n\n\n

Multiply the coordinates of point P<\/em>(–<\/sup>2, –<\/sup>2) by 5. The image is P<\/em>\u2032(–<\/sup>10, –<\/sup>10).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now multiply the coordinates of point Q<\/em>(–<\/sup>2, 2) by 5. The image is Q<\/em>\u2032(–<\/sup>10, 10).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now multiply the coordinates of points R<\/em>(1, 2) and S<\/em>(1, –<\/sup>2) by 5. The images are R<\/em>\u2032(5, 10) and S<\/em>\u2032(5, –<\/sup>10).<\/p>\n\n\n\n

The dilated points form a rectangle similar to PQRS<\/em>.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Write the coordinates of the vertices using arrow notation:<\/p>\n\n\n\n

\"\"<\/figure>\n<\/div><\/div>\n\n\n\n
\n
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Write the coordinates of the vertices after adilation with a scale factor of 1\/3,centred at the origin.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

The scale factor of a dilation is the ratio of a length in the image to the corresponding length in the original figure.<\/p>\n\n\n\n

This dilation is centred at the origin, so you can find the image by multiplying the x<\/em>– and y<\/em>-coordinates by the scale factor.<\/p>\n\n\n\n

Multiply the coordinates of point C<\/em>(–<\/sup>9, 0) by 1\/3. The image is C<\/em>\u2032(–<\/sup>3, 0).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now multiply the coordinates of point D<\/em>(–<\/sup>9, 6) by 1\/3.The image is D<\/em>\u2032(–<\/sup>3, 2).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now multiply the coordinates of points E<\/em>(9, 6) and F<\/em>(9, 0) by 1\/3.The images are E<\/em>\u2032(3, 2)and F<\/em>\u2032(3, 0).<\/p>\n\n\n\n

The dilated points form a rectangle similar to CDEF<\/em>.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Write the coordinates of the vertices using arrow notation:<\/p>\n\n\n\n

\"\"<\/figure>\n<\/div><\/div>\n\n\n\n
\n
\n

Write the coordinates of the vertices after a dilation with a scale factor of 3, centred at the origin.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

The scale factor of a dilation is the ratio of a length in the image to the corresponding length in the original figure.<\/p>\n\n\n\n

This dilation is centred at the origin, so you can find the image by multiplying the x<\/em>– and y<\/em>-coordinates by the scale factor.<\/p>\n\n\n\n

Multiply the coordinates of point L<\/em>(–<\/sup>2, –<\/sup>3) by 3. The image is L<\/em>\u2032(–<\/sup>6, –<\/sup>9).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now multiply the coordinates of point M<\/em>(3, –<\/sup>3) by 3. The image is M<\/em>\u2032(9, –<\/sup>9).<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now multiply the coordinates of point N<\/em>(–<\/sup>3, 3) by 3. The image is N<\/em>\u2032(–<\/sup>9, 9).<\/p>\n\n\n\n

The dilated points form a triangle similar to LMN<\/em>.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Write the coordinates of the vertices using arrow notation:<\/p>\n\n\n\n

\"\"<\/figure>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/canvas><\/canvas><\/p>\n\n\n\n

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\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
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\"\"<\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Dilations: find the coordinates A dilation enlarges or reduces a figure. Learn with an example Write the coordinates of the vertices after a dilation with a scale factor of 5, centred at the origin. The scale factor of a dilation is the ratio of a length in the image to the corresponding length in theContinue reading “N.8 Dilations: find the coordinates”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-277","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/277","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=277"}],"version-history":[{"count":13,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/277\/revisions"}],"predecessor-version":[{"id":17550,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/277\/revisions\/17550"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}