1.2 Translate point 86 places left and 6 places unt Translate point \( C 5 \) places right and 3 places down and name the image \( C \). Plot points \( P(2 ; 3), Q(-4 ; 2) \) and \( Q^{\prime}(5 ;-3) \) on a coordinate plane. 2.1 Translate point \( P 5 \) places down and 6 places left and name the image \( P^{\prime} \). 2.2 Describe a translation that will map point \( Q \) onto \( Q^{\prime} \). 3. Write the coordinates of the following points: 3.1 \( P^{\prime} \) if \( P(2 ; 3) \) is translated 4 places down.

Let's go through each part of your request step by step. ### 1. Translation of Point \( C \) You mentioned translating point \( C \) 5 places right and 3 places down. However, you didn't provide the coordinates of point \( C \). Let's assume the coordinates of point \( C \) are \( (x, y) \). The translation can be described as follows: - **Translation**: - Move 5 places right: \( x + 5 \) - Move 3 places down: \( y - 3 \) Thus, the new coordinates of point \( C \) after the translation will be \( (x + 5, y - 3) \). You can name the image \( C' \). ### 2. Plotting Points You want to plot the points \( P(2, 3) \), \( Q(-4, 2) \), and \( Q^{\prime}(5, -3) \) on a coordinate plane. - **Point \( P(2, 3) \)**: This point is located 2 units to the right of the origin and 3 units up. - **Point \( Q(-4, 2) \)**: This point is located 4 units to the left of the origin and 2 units up. - **Point \( Q^{\prime}(5, -3) \)**: This point is located 5 units to the right of the origin and 3 units down. ### 2.1 Translation of Point \( P \) You want to translate point \( P(2, 3) \) 5 places down and 6 places left. - **Translation**: - Move 6 places left: \( 2 - 6 = -4 \) - Move 5 places down: \( 3 - 5 = -2 \) Thus, the new coordinates of point \( P' \) will be \( (-4, -2) \). ### 2.2 Translation from \( Q \) to \( Q^{\prime} \) To describe a translation that maps point \( Q(-4, 2) \) onto point \( Q^{\prime}(5, -3) \): - **Translation**: - To find the horizontal movement: \( 5 - (-4) = 5 + 4 = 9 \) (9 places right) - To find the vertical movement: \( -3 - 2 = -5 \) (5 places down) So, the translation that maps point \( Q \) onto \( Q^{\prime} \) is 9 places right and 5 places down. ### 3. Coordinates of \( P^{\prime} \) If point \( P(2, 3) \) is translated 4 places down: - **Translation**: - Move 4 places down: \( 3 - 4 = -1 \) Thus, the new coordinates of point \( P^{\prime} \) will be \( (2, -1) \). ### Summary of Results - Image of \( C \): \( (x + 5, y - 3) \) (name it \( C' \)) - Coordinates of \( P' \): \( (-4, -2) \) - Translation from \( Q \) to \( Q^{\prime} \): 9 places right and 5 places down. - Coordinates of \( P^{\prime} \) after translating 4 places down: \( (2, -1) \)