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To determine which set of statements accurately explains how to plot the point [tex]\((-2.5, 3.75)\)[/tex], let's review the choices in detail:
1. Start at the origin. Move 2.5 units left because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex],-2.5 is between -2 and -3. Move 3.75 units up because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- Start at the origin [tex]\((0,0)\)[/tex].
- Move 2.5 units left (negative horizontal direction) because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex]. The fact that \[tex]$-2.5\$[/tex] is between -2 and -3 confirms this move.
- Move 3.75 units up (positive vertical direction) because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex]. The fact that \[tex]$3.75\$[/tex] is between 3 and 4 confirms this move.
2. Start at the origin. Move 2.5 units left because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex],-2.5 is between -2 and -3. Move 3.75 units down because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- The first move (2.5 units left) is correct.
- The second move (3.75 units down) is incorrect since a positive \[tex]$y\$[/tex]-coordinate indicates movement upward.
3. Start at the origin. Move 2.5 units up because the \[tex]$x\$[/tex]-coordinate is -2.5 . -2.5 is between -2 and -3. Move 3.75 units left because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- The first move (2.5 units up) is incorrect since movement in the \[tex]$x\$[/tex]-direction should be horizontal.
- The second move (3.75 units left) is also incorrect since movement in the \[tex]$y\$[/tex]-direction should be vertical.
4. Start at the origin. Move 2.5 units right because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex] .-2.5 is between -2 and -3. Move 3.75 units up because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- The first move (2.5 units right) is incorrect since the \[tex]$x\$[/tex]-coordinate is negative, which indicates movement to the left.
- The second move (3.75 units up) is correct, but due to the first error, this answer is incorrect.
Therefore, the set of statements that correctly explains how to plot the point at the location [tex]\((-2.5, 3.75)\)[/tex] is:
Start at the origin. Move 2.5 units left because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5,-2.5 is between -2 and -3. Move 3.75 units up because the \$[/tex]y\[tex]$-coordinate is \$[/tex]3.75\$ .3 .75 is between 3 and 4.
1. Start at the origin. Move 2.5 units left because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex],-2.5 is between -2 and -3. Move 3.75 units up because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- Start at the origin [tex]\((0,0)\)[/tex].
- Move 2.5 units left (negative horizontal direction) because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex]. The fact that \[tex]$-2.5\$[/tex] is between -2 and -3 confirms this move.
- Move 3.75 units up (positive vertical direction) because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex]. The fact that \[tex]$3.75\$[/tex] is between 3 and 4 confirms this move.
2. Start at the origin. Move 2.5 units left because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex],-2.5 is between -2 and -3. Move 3.75 units down because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- The first move (2.5 units left) is correct.
- The second move (3.75 units down) is incorrect since a positive \[tex]$y\$[/tex]-coordinate indicates movement upward.
3. Start at the origin. Move 2.5 units up because the \[tex]$x\$[/tex]-coordinate is -2.5 . -2.5 is between -2 and -3. Move 3.75 units left because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- The first move (2.5 units up) is incorrect since movement in the \[tex]$x\$[/tex]-direction should be horizontal.
- The second move (3.75 units left) is also incorrect since movement in the \[tex]$y\$[/tex]-direction should be vertical.
4. Start at the origin. Move 2.5 units right because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5\$[/tex] .-2.5 is between -2 and -3. Move 3.75 units up because the \[tex]$y\$[/tex]-coordinate is \[tex]$3.75\$[/tex] .3 .75 is between 3 and 4.
- The first move (2.5 units right) is incorrect since the \[tex]$x\$[/tex]-coordinate is negative, which indicates movement to the left.
- The second move (3.75 units up) is correct, but due to the first error, this answer is incorrect.
Therefore, the set of statements that correctly explains how to plot the point at the location [tex]\((-2.5, 3.75)\)[/tex] is:
Start at the origin. Move 2.5 units left because the \[tex]$x\$[/tex]-coordinate is \[tex]$-2.5,-2.5 is between -2 and -3. Move 3.75 units up because the \$[/tex]y\[tex]$-coordinate is \$[/tex]3.75\$ .3 .75 is between 3 and 4.
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