Question

each point of a figure is moved the same ______________________ and in the same ______________________.\\
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$(x,y) \longrightarrow (x + a, y + b)$\\
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example #2\\
$(x,y) \longrightarrow (x + 4, y + 2)$\\
$m(-5,-3) \longrightarrow$\\
$a(-2,-3) \longrightarrow$\\
$t(-2,-5) \longrightarrow$\\
$h(-5,-5) \longrightarrow$\\
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practice #1

Explanation:

For the fill - in - the - blank part:

Step1: Recall the definition of translation

In a translation (a type of transformation in geometry), each point of a figure is moved the same distance and in the same direction. The formula \((x,y)\to(x + a,y + b)\) represents a translation where \(a\) and \(b\) determine the horizontal and vertical distances (and thus the direction) of the move.

For the transformation of the points (Example #2):

Step1: Transform point \(M(-5,-3)\)

Using the rule \((x,y)\to(x + 4,y + 2)\), substitute \(x=-5\) and \(y = - 3\).
\(x+4=-5 + 4=-1\), \(y + 2=-3+2=-1\). So \(M(-5,-3)\to M'(-1,-1)\)

Step2: Transform point \(A(-2,-3)\)

Substitute \(x = - 2\) and \(y=-3\) into the rule \((x,y)\to(x + 4,y + 2)\).
\(x + 4=-2 + 4 = 2\), \(y+2=-3 + 2=-1\). So \(A(-2,-3)\to A'(2,-1)\)

Step3: Transform point \(T(-2,-5)\)

Substitute \(x=-2\) and \(y = - 5\) into the rule \((x,y)\to(x + 4,y + 2)\).
\(x + 4=-2+4 = 2\), \(y + 2=-5 + 2=-3\). So \(T(-2,-5)\to T'(2,-3)\)

Step4: Transform point \(H(-5,-5)\)

Substitute \(x=-5\) and \(y=-5\) into the rule \((x,y)\to(x + 4,y + 2)\).
\(x + 4=-5 + 4=-1\), \(y + 2=-5+2=-3\). So \(H(-5,-5)\to H'(-1,-3)\)

Answer:

• Fill - in - the - blank: distance, direction
• Point transformations: \(M(-5,-3)\to(-1,-1)\), \(A(-2,-3)\to(2,-1)\), \(T(-2,-5)\to(2,-3)\), \(H(-5,-5)\to(-1,-3)\)