Question 4

We will use the given coordinates and dimensions to find the dining room and table coordinates.

Step 1 — Dining Room Corners

Let's find the coordinates of points P and A from the diagram. Point P is at (-6, 0). Point A is at (12, 0). The length of the dining room is given as 18 ft. Let's check this length using the coordinates.

$PA \text{ length} = x_A - x_P$

$= 12 - (-6)$

$= 12 + 6$

$\boxed{18 \text{ ft}}$

This matches the given length. The dining room is 15 ft wide. It lies below the line segment PA. So, its y-coordinates will be negative. The y-coordinate of P and A is 0. The bottom corners will have a y-coordinate of $\mathbf{0 - 15 = -15}$. Let's name the other two corners Q and S. Point Q will be directly below A. Point S will be directly below P. The coordinates of Q are (12, -15). The coordinates of S are (-6, -15).

Step 2 — Dining Table Coordinates

First, we find the center of the dining room. The x-coordinates range from -6 to 12. The y-coordinates range from 0 to -15.

$x\text{-coordinate of center} = \frac{-6 + 12}{2}$

$= \frac{6}{2}$

$= 3$

$y\text{-coordinate of center} = \frac{0 + (-15)}{2}$

$= \frac{-15}{2}$

$= -7.5$

The center of the dining room is at (3, -7.5). The dining table is 5 ft × 3 ft. Let's assume the length is along the x-axis and width along the y-axis. Half of the length is $\mathbf{5/2 = 2.5}$ ft. Half of the width is $\mathbf{3/2 = 1.5}$ ft. Now we find the coordinates of the table's feet. These are the four corners of the table.

$x_{\text{left}} = 3 - 2.5 = 0.5$

$x_{\text{right}} = 3 + 2.5 = 5.5$

$y_{\text{bottom}} = -7.5 - 1.5 = -9$

$y_{\text{top}} = -7.5 + 1.5 = -6$

The four corners are: (x_left, y_bottom) = (0.5, -9) (x_right, y_bottom) = (5.5, -9) (x_right, y_top) = (5.5, -6) (x_left, y_top) = (0.5, -6)

Answer

(i) The coordinates of the dining room corners are: (-6, 0), (12, 0), (12, -15), (-6, -15). (ii) The coordinates of the four feet of the dining table are: (0.5, -9), (5.5, -9), (5.5, -6), (0.5, -6).