Question

1. rectangle abcd has consecutive vertices a(-7, 2), b(-7, 8), and c(-3, 8). find the coordinates of vertex d. (example 1)

Explanation:

Step1: Identify rectangle side properties

In a rectangle, opposite sides are equal and parallel. So, the horizontal change from $B$ to $C$ equals the horizontal change from $A$ to $D$, and the vertical change from $B$ to $C$ equals the vertical change from $A$ to $D$.

Step2: Calculate horizontal shift from B to C

The x-coordinate of $B$ is $-7$, x-coordinate of $C$ is $-3$. The shift is $-3 - (-7) = 4$.

Step3: Calculate vertical shift from B to C

The y-coordinate of $B$ is $8$, y-coordinate of $C$ is $8$. The shift is $8 - 8 = 0$.

Step4: Apply shifts to point A

Add the horizontal and vertical shifts to coordinates of $A(-7,2)$:
x-coordinate: $-7 + 4 = -3$
y-coordinate: $2 + 0 = 2$

Answer:

$(-3, 2)$