Question

lesson 4 practice problems

1. a. here is a grid with points.

what are the coordinates of a, b, and c after a translation to the right by 4 units and up 1 unit? plot these points on the grid, and label them a, b and c.
b. here are some points.
what are the coordinates of d, e, and f after a reflection over the y - axis? plot these points on the grid, and label them d, e and f.

Explanation:

Step1: Recall translation rule

For a translation to the right by \(a\) units and up by \(b\) units, the rule for a point \((x,y)\) is \((x + a,y + b)\). Here \(a = 4\) and \(b=1\).

Step2: Assume initial - coordinates of \(A\), \(B\), \(C\)

Let's assume \(A=(x_1,y_1)\), \(B=(x_2,y_2)\), \(C=(x_3,y_3)\). After translation, \(A'=(x_1 + 4,y_1+1)\), \(B'=(x_2 + 4,y_2 + 1)\), \(C'=(x_3 + 4,y_3+1)\). Plot these points on the grid.

Step3: Recall reflection rule

For a reflection over the \(y\) - axis, the rule for a point \((x,y)\) is \((-x,y)\).

Step4: Assume initial - coordinates of \(D\), \(E\), \(F\)

Let \(D=(x_4,y_4)\), \(E=(x_5,y_5)\), \(F=(x_6,y_6)\). After reflection over the \(y\) - axis, \(D'=(-x_4,y_4)\), \(E'=(-x_5,y_5)\), \(F'=(-x_6,y_6)\). Plot these points on the grid.

Since we don't have the actual initial coordinates of the points from the image, we can't give specific numerical answers. But the general methods for transformation are as above. If we had the initial coordinates, for example, if \(A=(1,2)\):

(with example for \(A\)):

Step1: Apply translation rule

For \(A=(1,2)\), \(a = 4\), \(b = 1\). Using \((x + a,y + b)\), we get \(A'=(1 + 4,2+1)=(5,3)\).

Step2: Assume \(D=( - 2,3)\)

For reflection over the \(y\) - axis, using \((-x,y)\), \(D'=-(-2),3=(2,3)\).

Answer:

Without the initial - coordinates of points \(A\), \(B\), \(C\), \(D\), \(E\), \(F\) from the grid, we can't give specific numerical coordinates for \(A'\), \(B'\), \(C'\), \(D'\), \(E'\), \(F'\). But if \(A=(x_1,y_1)\), \(A'=(x_1 + 4,y_1+1)\); if \(D=(x_4,y_4)\), \(D'=(-x_4,y_4)\) and similar for other points.