\( \triangle A B C \) will undergo two transformations to give \( \triangle A^{\prime} B^{\circ} C \). Which pair of transformations will give a different image of \( \triangle A B C \) if the order of transformations is reversed? A. a rotation \( 90^{\circ} \) counterclockwise about the origin followed by a reflection across the \( y \)-axis B. a translation 5 units down followed by a translation 4 units to the right C. a reflection across the \( x \)-axis followed by a reflection across the \( y \)-axis D. a rotation \( 180^{\circ} \) clockwise about the origin followed by a reflection across the \( y \)-axis

7. En cada ítem, estudiar la posición relativa entre las dos rectas dadas y graficar ambas en un mismo sistema de coordenadas cartesianas. a) \( \left\{\begin{array}{l}x=1-5 \lambda \\ y=2+3 \lambda \\ z=-5+\lambda\end{array}\left\{\begin{array}{l}x=1 \\ y=1 \\ z=\mu\end{array}(\lambda, \mu \in \mathbb{R})\right.\right. \)\( \quad \) b) \( \left\{\begin{array}{l}x=3+2 \alpha \\ y=1-\alpha \\ z=5\end{array} \quad\left\{\begin{array}{l}x=-1-6 \beta \\ y=3+3 \beta \\ z=5\end{array} \quad(\alpha, \beta \in \mathbb{R})\right\}\right. \)

10.A circle, centre \( C \), has a diameter \( P Q \) where \( P \) is the point \( (-1,-1) \) and \( Q \) is the point \( (5,7) \). (a) Show that the equation of the circle is \( x^{2}+y^{2}-4 x-6 y-12=0 \).

7. En cada ítem, estudiar la posición relativa entre las dos rectas dadas y graficar ambas en un mismo sistema de coordenadas cartesianas. a) \( \left\{\begin{array}{l}x=1-5 \lambda \\ y=2+3 \lambda \\ z=-5+\lambda\end{array}\left\{\begin{array}{l}x=1 \\ y=1 \\ z=\mu\end{array}(\lambda, \mu \in \mathbb{R})\right.\right. \)

b. La figura se armó con cubos cuyas aristas miden \( 3,5 \mathrm{~cm} \). Respuesta: ¿Cuál es el el volumen de la figura compuesta? de uno de los cubos?

Find the slope of the line passing through the given points. (If an answer is undefined, enter UNDEFINED.) \[ (7,-4) \text { and }(7,-3) \]