This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths (|x₂-x₁| if y-coordinates are the same, |y₂-y₁| if x-coordinates are the same). To draw the rectangle, plot the vertices as ordered pairs A(2,1), B(7,1), C(7,5), and D(2,5), connect consecutive vertices with line segments, and close the polygon by connecting the last back to the first. Finding side lengths for axis-aligned sides: horizontal sides AB and DC have the same y-coordinates (y=1 and y=5), so length = |7-2| = 5 using x-coordinate difference; vertical sides BC and DA have the same x-coordinates (x=7 and x=2), so length = |5-1| = 4 using y-difference, with absolute value ensuring positive length. For example, the perimeter is calculated by adding all sides: 5 + 4 + 5 + 4 = 18 units, or 2 × (length + width) = 2 × (5 + 4) = 18 units. The correct answer is 18 units, as it matches the perimeter calculation for the dog park. A common error is miscalculating the differences, like |7-2| = 4 instead of 5, leading to an incorrect perimeter. To draw accurately: (1) identify axes and scale, (2) plot each vertex by counting x units right or left from the origin and y units up or down, (3) connect in order from A to B to C to D and back to A, (4) verify the shape is closed; for perimeter, sum the calculated side lengths using the appropriate differences and absolute values.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths (|x₂ - x₁| if y-coordinates are the same, |y₂ - y₁| if x-coordinates are the same). To draw the rectangle, plot the vertices as ordered pairs A(-3,-1), B(2,-1), C(2,3), and D(-3,3), connect consecutive vertices with line segments in the order A to B to C to D back to A, and close the polygon. For side lengths of axis-aligned sides, calculate horizontal sides like A to B with the same y-coordinate of -1, length |2 - (-3)| = 5 using the x-difference, and vertical sides like B to C with the same x-coordinate of 2, length |3 - (-1)| = 4 using the y-difference; absolute value ensures positive length. For this rectangle, plot the points, connect them to form sides of lengths 5 (horizontal), 4 (vertical), 5 (horizontal), and 4 (vertical), so the perimeter is 5 + 4 + 5 + 4 = 18 units, matching choice B. A common error is using the wrong coordinate difference, such as y-difference for a horizontal side instead of x-difference, leading to incorrect lengths like | -1 - (-1)| = 0 for A to B. To draw accurately: (1) identify axes and scale, (2) plot each vertex by counting x units right or left from the origin and y units up or down, (3) connect in order, and (4) verify the shape is closed. For side lengths and perimeter: (1) identify horizontal or vertical sides, (2) use the appropriate difference with absolute value, (3) sum all sides for perimeter, and remember applications like area would be base × height = 5 × 4 = 20 square units, while avoiding mistakes like forgetting absolute value or arithmetic errors.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths with formulas like |x₂ - x₁| if y-coordinates are the same or |y₂ - y₁| if x-coordinates are the same. To draw the rectangle, plot the vertices as ordered pairs A(-3,2), B(4,2), C(4,-1), and D(-3,-1), connect consecutive vertices with line segments in order, and close the polygon by connecting the last point back to the first. For side lengths, the horizontal side AB from (-3,2) to (4,2) has the same y=2, so length = |4 - (-3)| = 7 units using the x-difference, while vertical sides like BC from (4,2) to (4,-1) have the same x=4, so length = |-1 - 2| = 3 units using the y-difference, with absolute values ensuring positive lengths. For this ramp rectangle, the correct length of side AB is 7 units. A common error is forgetting to add the absolute value for negative coordinates, such as calculating 4 - (-3) as 1 instead of 7, or using y-differences for horizontal sides. To draw accurately: (1) identify the axes and scale, including negative values, (2) plot each vertex carefully, (3) connect in order, and (4) verify closure. For side lengths: (1) identify horizontal or vertical alignment, (2) use the appropriate difference, (3) calculate with absolute value, noting applications like material needs for the ramp, and avoiding mistakes like coordinate reversal or arithmetic errors.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths (|x₂ - x₁| if y-coordinates are the same, |y₂ - y₁| if x-coordinates are the same). To draw the rectangle, plot the vertices as ordered pairs P(1,-4), Q(1,2), R(5,2), and S(5,-4), connect consecutive vertices with line segments in the order P to Q to R to S back to P, and close the polygon. For side lengths of axis-aligned sides, vertical sides like P to Q have the same x-coordinate of 1, length |2 - (-4)| = 6 using the y-difference, and horizontal sides like Q to R have the same y-coordinate of 2, length |5 - 1| = 4 using the x-difference; absolute value ensures positive length. For this rectangle, plot and connect to find lengths 6 (vertical), 4 (horizontal), 6 (vertical), and 4 (horizontal), so the area is base × height = 4 × 6 = 24 square units, matching choice A. A common error is plotting coordinates reversed, like treating (1,-4) as (-4,1), or using x-difference for vertical sides, leading to wrong area like 6 × 6 = 36. To draw accurately: (1) identify axes and scale, (2) plot each vertex carefully, (3) connect in order, and (4) verify closed. For applications like area: calculate side lengths first, then multiply for rectangles, while for perimeter sum them (here 6 + 4 + 6 + 4 = 20 units), avoiding arithmetic errors or forgetting to close the polygon.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths (|x₂-x₁| if y-coordinates are the same, |y₂-y₁| if x-coordinates are the same). To draw the rectangle, plot the vertices as ordered pairs (-4,-1), (2,-1), (2,3), and (-4,3), connect consecutive vertices with line segments, and close the polygon by connecting the last back to the first. Finding side lengths for axis-aligned sides: the horizontal side from (-4,-1) to (2,-1) has the same y-coordinate (y=-1), so length = |2 - (-4)| = |6| = 6 using x-coordinate difference; absolute value ensures positive length. For example, if the points were (1,1) and (5,1), the length would be |5-1| = 4 units. The correct length of the specified horizontal side is 6 units. A common error is forgetting the absolute value and getting a negative length like 2 - (-4) = 6 but misapplying signs, or using y-differences instead of x for horizontal sides. To calculate side lengths: (1) identify if horizontal or vertical by checking coordinates, (2) use the appropriate difference (|x₂-x₁| for horizontal), (3) compute the value, (4) ensure it's positive with absolute value.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths with formulas like |x₂ - x₁| if y-coordinates are the same or |y₂ - y₁| if x-coordinates are the same. To draw the bulletin board, plot the vertices as ordered pairs (-1,-2), (5,-2), (5,1), and (-1,1), connect consecutive vertices with line segments in order, and close the polygon by connecting the last point back to the first. For side lengths, horizontal sides like from (-1,-2) to (5,-2) have the same y=-2, so length = |5 - (-1)| = 6 units, while vertical sides like from (5,-2) to (5,1) have the same x=5, so length = |1 - (-2)| = 3 units, with absolute values ensuring positive lengths. For this bulletin board, the perimeter is 2 × (6 + 3) = 18 units. A common error is ignoring negative signs, such as calculating width as 5 - 1 = 4 instead of 6, leading to perimeters like 14 units. To draw accurately: (1) handle negative coordinates on axes, (2) plot each point, (3) connect in order, and (4) check closure. For perimeter: (1) identify side types, (2) calculate differences, (3) sum all, noting uses like border length, and avoiding errors like missing absolute values or wrong arithmetic.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths (|x₂ - x₁| if y-coordinates are the same, |y₂ - y₁| if x-coordinates are the same). To draw the rectangle, plot the vertices as ordered pairs (2,1), (7,1), (7,5), and (2,5), connect consecutive vertices with line segments, and close the polygon. For side lengths of axis-aligned sides, horizontal sides have the same y, length |7 - 2| = 5 using x-difference, and vertical sides have the same x, length |5 - 1| = 4 using y-difference; absolute value ensures positive length. For this bulletin board rectangle, lengths are 5, 4, 5, 4, so perimeter is 5 + 4 + 5 + 4 = 18 units, matching choice A. A common error is arithmetic like |7-2|=4, or using y for horizontal leading to wrong perimeter. To draw accurately: (1) identify axes and scale, (2) plot vertices, (3) connect in order, (4) verify closed. For perimeter: sum calculated side lengths, or for area 5 × 4 = 20 square units, avoiding mistakes like forgetting absolute value or not closing the polygon.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths with formulas like |x₂ - x₁| if y-coordinates are the same or |y₂ - y₁| if x-coordinates are the same, and calculating area. To draw the rectangle, plot the vertices as ordered pairs A(1,-3), B(6,-3), C(6,2), and D(1,2), connect consecutive vertices with line segments in order, and close the polygon by connecting the last point back to the first. For side lengths, horizontal sides like AB from (1,-3) to (6,-3) have the same y=-3, so length = |6-1| = 5 units, while vertical sides like BC from (6,-3) to (6,2) have the same x=6, so length = |2 - (-3)| = 5 units. The area of the rectangle is 5 × 5 = 25 square units. A common error is miscalculating height as 2 - 3 = -1 or forgetting the negative, leading to areas like 20 or 15. To draw accurately: (1) include negative y on axes, (2) plot vertices, (3) connect, (4) verify. For area: (1) find lengths, (2) multiply, noting uses like coverage, while diagonals are advanced, and avoiding mistakes like no absolute value or wrong differences.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths (|x₂-x₁| if y-coordinates are the same, |y₂-y₁| if x-coordinates are the same). To draw the rectangle, plot the vertices as ordered pairs A(3,-2), B(3,4), C(-1,4), and D(-1,-2), connect consecutive vertices with line segments, and close the polygon by connecting the last back to the first. Finding side lengths for axis-aligned sides: vertical sides AB and DC have lengths |4 - (-2)| = 6; horizontal sides BC and DA have lengths |-1 - 3| = 4; absolute value ensures positive length. For example, area = length × width = 6 × 4 = 24 square units. The correct area is 24 square units. A common error is mixing up horizontal and vertical calculations. To find area: determine base and height from differences, multiply, and confirm with plot.

This question tests drawing polygons on a coordinate plane given vertex coordinates, using coordinates to find horizontal and vertical side lengths (|x₂ - x₁| if y-coordinates are the same, |y₂ - y₁| if x-coordinates are the same). To draw the rectangle, plot the vertices as ordered pairs A(-1,-1), B(5,-1), C(5,2), and D(-1,2), connect consecutive vertices with line segments, and close the polygon. For side lengths, horizontal sides like A to B have same y=-1, length |5 - (-1)|=6 using x-difference, vertical like B to C have same x=5, length |2 - (-1)|=3 using y-difference; absolute value ensures positive length. For this rectangle, area is base × height = 6 × 3 = 18 square units, matching choice C. A common error is wrong arithmetic like |5 - (-1)|=4, leading to area 12, or using vertical for base incorrectly. To draw accurately: (1) identify axes and scale, (2) plot vertices, (3) connect in order, (4) verify closed. For area: calculate lengths first, then multiply, with perimeter 6+3+6+3=18 units, avoiding mistakes like forgetting to close or missing absolute value.