Question

exercises 13-1
for exercises 1-6, give the coordinates of each point and name the quadrant (if any) in which it is located.

1. k
2. l
3. m
4. n
5. p
6. q

Explanation:

Identify the orientation and axes of the coordinate system

The coordinate grid is rotated \(90^\circ\) clockwise.

• The horizontal axis is labeled \(y\) with positive values to the right and negative values to the left.
• The vertical axis is labeled \(x\) with positive values pointing downwards and negative values pointing upwards.
• Standard ordered pairs are written as \((x, y)\).

Determine the coordinates of each point

• Point \(K\): Located at vertical position \(x = -6\) and horizontal position \(y = -4\). Thus, \((-6, -4)\).
• Point \(L\): Located at vertical position \(x = 0\) and horizontal position \(y = 2\). Thus, \((0, 2)\).
• Point \(M\): Located at vertical position \(x = 4\) and horizontal position \(y = -5\). Thus, \((4, -5)\).
• Point \(N\): Located at vertical position \(x = -5\) and horizontal position \(y = 0\). Thus, \((-5, 0)\).
• Point \(P\): Located at vertical position \(x = 7\) and horizontal position \(y = 6\). Thus, \((7, 6)\).
• Point \(Q\): Located at vertical position \(x = 1\) and horizontal position \(y = -8\). Thus, \((1, -8)\).

Determine the quadrant or axis location for each point

• Point \(K(-6, -4)\): Both \(x < 0\) and \(y < 0\), which is Quadrant III.
• Point \(L(0, 2)\): Located on the \(y\)-axis (no quadrant).
• Point \(M(4, -5)\): \(x > 0\) and \(y < 0\), which is Quadrant IV.
• Point \(N(-5, 0)\): Located on the \(x\)-axis (no quadrant).
• Point \(P(7, 6)\): Both \(x > 0\) and \(y > 0\), which is Quadrant I.
• Point \(Q(1, -8)\): \(x > 0\) and \(y < 0\), which is Quadrant IV.

Answer:

No.	Point	Coordinates	Quadrant / Location
2	\(L\)	\((0, 2)\)	\(y\)-axis
3	\(M\)	\((4, -5)\)	Quadrant IV
4	\(N\)	\((-5, 0)\)	\(x\)-axis
5	\(P\)	\((7, 6)\)	Quadrant I
6	\(Q\)	\((1, -8)\)	Quadrant IV