Question

points a - h in the standard (x,y) coordinate plane below all have integer coordinates.

1. which of the following points has the coordinates (-2,3)?

a. a
b. b
c. e
d. f
e. h

1. which of the following line segments is not perpendicular to (overline{ad})?

f. (overline{ah})
g. (overline{cf})
h. (overline{bg})
j. (overline{bc})
k. (overline{de})

Explanation:

Step1: Understand coordinate rules

In the coordinate - plane, the first number in an ordered pair $(x,y)$ is the $x$ - coordinate (horizontal position) and the second is the $y$ - coordinate (vertical position). For the point $(-2,3)$, we move 2 units to the left of the origin (since $x=-2$) and 3 units up (since $y = 3$). Looking at the points $A - H$, point $A$ has coordinates $(-2,3)$.

Step2: Analyze perpendicular lines

The line segment $\overline{AD}$ is a horizontal line (since the $y$ - coordinates of points $A$ and $D$ are the same). A line perpendicular to a horizontal line is a vertical line. Among the given line - segments, $\overline{BC}$ is a vertical line, $\overline{AH}$ is a vertical line, $\overline{CF}$ is a vertical line, $\overline{BG}$ is a vertical line. The line segment $\overline{DE}$ is a horizontal line, so it is not perpendicular to $\overline{AD}$.

Answer:

1. A. $A$
2. K. $\overline{DE}$