A triangle has corners at #(2, 5 )#, #( 1, 3 )#, and #( 4 , 2 )#. If the triangle is dilated by # 7 x# around #(1, 3)#, what will the new coordinates of its corners be?

Question

A triangle has corners at #(2, 5 )#, #( 1, 3  )#, and #( 4 , 2  )#.  If the triangle is dilated by # 7   x# around #(1, 3)#, what will the new coordinates of its corners be?

Savannah Aguilar · Accepted Answer

Simply multiply the coordinates by the scaling factor, in this case 7.
(14, 35), (7, 21) and (28, 14)

First have the vertices written and magnify each of the vertices by the magnify factor (or scaling factor) #A (2,5) =>_(xx7) A'(14,35) # #B (1,3) =>_(xx 7) B'(7,21)# #C (4,2) =>_(xx 7) C'(28,14)#

Evelyn Arboleda · Answer

undefined To dilate a triangle by a factor of 7 around the point (1, 3), we'll use the dilation formula:

New_x = center_x + dilation_factor * (original_x - center_x)
New_y = center_y + dilation_factor * (original_y - center_y)

For the point (2, 5):
New_x = 1 + 7 * (2 - 1) = 8
New_y = 3 + 7 * (5 - 3) = 17

For the point (1, 3):
New_x = 1 + 7 * (1 - 1) = 1
New_y = 3 + 7 * (3 - 3) = 3

For the point (4, 2):
New_x = 1 + 7 * (4 - 1) = 22
New_y = 3 + 7 * (2 - 3) = -4

So, the new coordinates of the triangle's corners after dilation are:
(8, 17), (1, 3), and (22, -4).