Question

complete problems 3–5.
3 a map is shown in the coordinate plane, with city hall at the origin.
a. to plot the point for a library at (2, -3), move 2 units ____ and 3 units ____ from the origin.
b. a movie theater is located 4 units left and 4 units up from city hall. plot a point to show the location of the movie theater and label the point with its coordinates.

Explanation:

Step1: Analyze part (a)

In a coordinate plane, the x - coordinate determines the horizontal movement (right is positive, left is negative) and the y - coordinate determines the vertical movement (up is positive, down is negative). For the point \((2,-3)\), the x - coordinate is 2 (positive, so move right) and the y - coordinate is - 3 (negative, so move down). So we move 2 units right and 3 units down from the origin.

Step2: Analyze part (b)

Moving left 4 units from the origin (City Hall) means the x - coordinate is - 4 (since left is negative on the x - axis). Moving up 4 units means the y - coordinate is 4 (since up is positive on the y - axis). So the coordinates of the movie theater are \((-4,4)\). To plot the point, we find the position on the coordinate plane where \(x=-4\) and \(y = 4\) and mark it, then label it with \((-4,4)\).

Answer:

a. right, down; b. The point for the movie theater is plotted at \((-4,4)\) on the coordinate plane (4 units left (along the negative x - axis) and 4 units up (along the positive y - axis) from the origin) and labeled as \((-4,4)\).