Question

1. graph the image of the triangle below using a scale factor of ( k = 4 ).

( s(__,__) )
( t(__,__) )
( u(__,__) )

Explanation:

Step1: Find the coordinates of \(S\), \(T\), \(U\)

Assume \(S=(0,0)\), \(T=(3,4)\), \(U=(3,0)\) (by observing the grid - points).

Step2: Use the scale - factor formula for dilation

If a point \((x,y)\) is dilated with a scale factor \(k\), the new point \((x',y')=(kx,ky)\).
For point \(S=(0,0)\):
\(x' = k\times x=4\times0 = 0\), \(y'=k\times y = 4\times0=0\), so \(S'=(0\times4,0\times4)=(0,0)\)
For point \(T=(3,4)\):
\(x'=k\times x = 4\times3=12\), \(y'=k\times y=4\times4 = 16\), so \(T'=(3\times4,4\times4)=(12,16)\)
For point \(U=(3,0)\):
\(x'=k\times x=4\times3 = 12\), \(y'=k\times y=4\times0=0\), so \(U'=(3\times4,0\times4)=(12,0)\)

Answer:

\(S'(0,0)\), \(T'(12,16)\), \(U'(12,0)\)