Question

(show work for every problem.)

1. plot the points \\((7, 1)\\), \\((2, -3)\\), \\((5, 0)\\), \\((-2, 6)\\), and \\((-4, -5)\\) on the coordinate plane below.

Explanation:

Identify the given points

Using the Ordered Pairs knowledge point
The problem requires plotting the following five ordered pairs on the Cartesian coordinate plane:

$$ (7, 1), \quad (2, -3), \quad (5, 0), \quad (-2, 6), \quad (-4, -5) $$

Determine the quadrant or axis for each point

Using the Coordinate Quadrants knowledge point

• \((7, 1)\): Both coordinates are positive, so it lies in Quadrant I.
• \((2, -3)\): \(x > 0\) and \(y < 0\), so it lies in Quadrant IV.
• \((5, 0)\): \(y = 0\), so it lies on the positive \(x\)-axis.
• \((-2, 6)\): \(x < 0\) and \(y > 0\), so it lies in Quadrant II.
• \((-4, -5)\): Both coordinates are negative, so it lies in Quadrant III.

Plot each coordinate on the grid

Using the Data Point Plotting knowledge point

• For \((7, 1)\): Start at the origin \((0,0)\), move \(7\) units right, and \(1\) unit up.
• For \((2, -3)\): Start at \((0,0)\), move \(2\) units right, and \(3\) units down.
• For \((5, 0)\): Start at \((0,0)\), move \(5\) units right, and stay on the \(x\)-axis.
• For \((-2, 6)\): Start at \((0,0)\), move \(2\) units left, and \(6\) units up.
• For \((-4, -5)\): Start at \((0,0)\), move \(4\) units left, and \(5\) units down.

Answer:

The five points are plotted on the coordinate plane at the following locations:

• \((7, 1)\) is located in Quadrant I (7 units right, 1 unit up).
• \((2, -3)\) is located in Quadrant IV (2 units right, 3 units down).
• \((5, 0)\) is located on the positive \(x\)-axis (5 units right, 0 units up/down).
• \((-2, 6)\) is located in Quadrant II (2 units left, 6 units up).
• \((-4, -5)\) is located in Quadrant III (4 units left, 5 units down).