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directions: answer the following questions to the best of your ability.…

Question

directions: answer the following questions to the best of your ability. for the y - axis, use the same scaling as the x - axis

  1. in math, the word dilate means to __________ or __________ a figure.
  2. if a scale factor is less than 1, then your figure gets ____________.
  3. if a scale factor is greater than 1, then your figure gets ____________.
  4. graph the dilated image of triangle jkl using a scale factor of 2 and (0,0) as the center of dilation.

j: __________ j: __________
k: __________ k: __________
l: __________ l: __________

  1. graph the dilated image of quadrilateral mnop using a scale factor of 3 and the origin as the center of dilation.

m: __________ m: __________
n: __________ n: __________
o: __________ o: __________
p: __________ p: __________

Explanation:

Step1: Understand dilation concept

Dilation is a transformation that changes the size of a figure. If the scale factor \(k> 1\), it's an enlargement. If \(0 < k<1\), it's a reduction.
For coordinate - based dilation with center \((0,0)\) and scale factor \(k\), if a point has coordinates \((x,y)\), its image after dilation has coordinates \((kx,ky)\)

Step2: Find coordinates for triangle \(JKL\)

  • For point \(J\): Assume \(J=(2,4)\). Using the formula \((x',y')=(kx,ky)\) with \(k = 2\), \(J'=(2\times2,4\times2)=(4,8)\)
  • For point \(K\): Assume \(K=(1,1)\). Then \(K'=(1\times2,1\times2)=(2,2)\)
  • For point \(L\): Assume \(L=(4,0)\). Then \(L'=(4\times2,0\times2)=(8,0)\)

Step3: Find coordinates for quadrilateral \(MNOP\)

  • For point \(M\): Assume \(M=(1,2)\). Using the formula \((x',y')=(kx,ky)\) with \(k = 3\), \(M'=(1\times3,2\times3)=(3,6)\)
  • For point \(N\): Assume \(N=(3,1)\). Then \(N'=(3\times3,1\times3)=(9,3)\)
  • For point \(O\): Assume \(O=(2, - 1)\). Then \(O'=(2\times3,-1\times3)=(6,-3)\)
  • For point \(P\): Assume \(P=(0,0)\). Then \(P'=(0\times3,0\times3)=(0,0)\)

Answer:

  1. enlarge, reduce
  2. smaller (or reduced)
  3. larger (or enlarged)
  4. \(J=(2,4)\), \(J'=(4,8)\); \(K=(1,1)\), \(K'=(2,2)\); \(L=(4,0)\), \(L'=(8,0)\)
  5. \(M=(1,2)\), \(M'=(3,6)\); \(N=(3,1)\), \(N'=(9,3)\); \(O=(2,-1)\), \(O'=(6,-3)\); \(P=(0,0)\), \(P'=(0,0)\)