Question

1. graph the image of the triangle below using a scale factor of k = 4.
2. graph the image of the rectangle below using a scale factor of k = 5/2.
3. graph the image of the quadrilateral below using a scale factor of k = 1/3.
4. graph the image of the triangle below using a scale factor of k = 3/4.
5. identify the scale factor used to graph the image below.
6. identify the scale factor used to graph the image below.

Explanation:

Step1: Recall the rule for dilation

To find the coordinates of the dilated image of a point $(x,y)$ with a scale - factor $k$, we use the formula $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Solve problem 7

Assume the coordinates of points $S(x_1,y_1)$, $T(x_2,y_2)$, $U(x_3,y_3)$. For a scale - factor $k = 4$, the new coordinates are $S'(4x_1,4y_1)$, $T'(4x_2,4y_2)$, $U'(4x_3,4y_3)$. But since the original coordinates are not given, we'll just state the general method.

Step3: Solve problem 8

For a rectangle with vertices $J(x_J,y_J)$, $K(x_K,y_K)$, $L(x_L,y_L)$, $M(x_M,y_M)$ and a scale - factor $k=\frac{5}{2}$, the new vertices are $J'(\frac{5}{2}x_J,\frac{5}{2}y_J)$, $K'(\frac{5}{2}x_K,\frac{5}{2}y_K)$, $L'(\frac{5}{2}x_L,\frac{5}{2}y_L)$, $M'(\frac{5}{2}x_M,\frac{5}{2}y_M)$.

Step4: Solve problem 9

For a quadrilateral with vertices $B(x_B,y_B)$, $C(x_C,y_C)$, $D(x_D,y_D)$, $E(x_E,y_E)$ and a scale - factor $k = \frac{1}{3}$, the new vertices are $B'(\frac{1}{3}x_B,\frac{1}{3}y_B)$, $C'(\frac{1}{3}x_C,\frac{1}{3}y_C)$, $D'(\frac{1}{3}x_D,\frac{1}{3}y_D)$, $E'(\frac{1}{3}x_E,\frac{1}{3}y_E)$.

Step5: Solve problem 10

For a triangle with vertices $X(x_X,y_X)$, $Y(x_Y,y_Y)$, $Z(x_Z,y_Z)$ and a scale - factor $k=\frac{3}{4}$, the new vertices are $X'(\frac{3}{4}x_X,\frac{3}{4}y_X)$, $Y'(\frac{3}{4}x_Y,\frac{3}{4}y_Y)$, $Z'(\frac{3}{4}x_Z,\frac{3}{4}y_Z)$.

Step6: Solve problem 11

To find the scale - factor $k$, if we know a pair of corresponding points $(x,y)$ and $(x',y')$ of the original and dilated figures, we use the formula $k=\frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$ and $y
eq0$). Without the actual coordinates, we can't calculate the exact value, but this is the method.

Step7: Solve problem 12

Similarly, for a pair of corresponding points $(x,y)$ and $(x',y')$ of the original and dilated figures, use the formula $k = \frac{x'}{x}=\frac{y'}{y}$ (assuming $x
eq0$ and $y
eq0$) to find the scale - factor.

Since the original coordinates of the points in the figures are not given, we can't provide the exact numerical answers for the coordinates of the dilated points and the scale - factors. If the coordinates were provided, we would substitute them into the above - mentioned formulas.

Answer:

For problems 7 - 10, we need the original coordinates of the vertices of the figures to find the coordinates of the dilated figures. For problems 11 - 12, we need the coordinates of a pair of corresponding points of the original and dilated figures to find the scale - factor.