Question

question 5 (multiple choice worth 1 points) (82.01r lc) the coordinate grid below shows triangle abc and its image after translation, triangle abc which of the following completes the rule for this translation, (x, y) → (x + 6, ____)? y - 6 y + 6 y - 8 y + 8

Explanation:

Step1: Find the y - coordinate of a point

Take point \(B\). Let's assume the coordinates of \(B\) are \((x_1,y_1)\) and the coordinates of \(B'\) are \((x_2,y_2)\). Suppose \(B(-5,5)\) and \(B'(1,-1)\) (by observing the graph).

Step2: Calculate the change in y - coordinate

The formula for the translation of a point \((x,y)\to(x + a,y + b)\). We know \(x_2=x_1 + 6\) (since \(1=-5 + 6\)). For the \(y\) - coordinate, we use \(y_2=y_1 + b\). Substituting \(y_1 = 5\) and \(y_2=-1\), we get \(-1=5 + b\). Solving for \(b\): \(b=-1 - 5=-6\).

Answer:

\(y - 6\)