This question tests quadrant identification by plotting points and checking coordinate signs. R(7,1) in I, S(-2,9) in II (x negative, y positive), T(-6,-4) in III, U(4,-8) in IV; thus, Quadrant II is S(-2,9), choice D. This demonstrates all quadrants without distance elements. Errors could stem from sign confusion, like mistaking IV for II. Practice with mixed signs reinforces quadrant rules. Plotting helps visualize the plane's division. Real-world uses include navigation systems assigning zones.

This question tests graphing points in all four quadrants and calculating vertical distances on a grid representing city blocks (|y₂-y₁| when same x). Graphing: plot ordered pair (x,y) by moving x horizontally from origin (left if negative, right if positive), then y vertically (down if negative, up if positive), marks point in appropriate quadrant (signs determine which: I both +, II x− y+, III both −, IV x+ y−). For (−3,2) and (−3,-5), same x=-3, vertical distance |2-(-5)|=|7|=7 blocks, matching choice B. Correct calculation uses absolute value for positive distance along vertical street. Common errors: no absolute value (2-(-5)=7, but reverse gives -7 claimed as distance), or arithmetic mistake like |2+5|=7 but misadding. Distance tips: for same x, |y difference|; real-world like navigating city grids vertically.

This question tests calculating horizontal distances between points with same y-coordinate using absolute value. Points with same y are on a horizontal line, distance = |x₂ - x₁|, always positive. For R(-4,3) and S(2,3) on y=3, distance = |2 - (-4)| = |6| = 6 units, matching choice B. Correct calculation uses x-difference with absolute value. Errors like |2 + (-4)| = | -2 | =2, or using y (|3-3|=0), or no absolute value. Distance steps: check same y, use |x₂ - x₁|. Real-world application: measuring east-west distances on maps.

This question tests calculating horizontal distances between points with the same y-coordinate using the absolute value of the difference in x-coordinates. Points with the same y-coordinate lie on a horizontal line, so the distance is |x₂ - x₁|, which always gives a positive result. For P(-6,4) and Q(3,4), both at y=4, the distance is |3 - (-6)| = |9| = 9 units, matching choice B. This is useful in applications like sensor placements on a grid for coverage measurement. Common mistakes include using y-coordinates instead of x, as in D, or omitting absolute value to get negative distances like in C. Practice by confirming same y for horizontal and applying |x₂ - x₁|. Remember, order of subtraction doesn't matter due to absolute value, ensuring consistent positive distances.

This question tests recognizing points on the same horizontal line (same y-coordinate) for distance calculation using |x₂ - x₁|. Horizontal lines have constant y, so pairs like T₁(-8,6) and T₂(5,6) share y=6, fitting choice C. Verify by checking y-values; T₃ and T₄ also share y=-3, but the question asks for one pair. This differs from vertical pairs like T₁ and T₃ (same x=-8), which use |y₂ - y₁|. Mistakes include confusing horizontal with vertical or picking diagonal pairs. Practice identifying shared coordinates to apply the correct distance formula. In game maps, this helps plan straight-line paths efficiently.

This question tests calculating vertical distances between points with the same x-coordinate using the absolute value of the difference in y-coordinates. Points with the same x-coordinate lie on a vertical line, so the distance is |y₂ - y₁|, ensuring a positive value regardless of order. For A(2,7) and B(2,-1), both at x=2, the distance is |7 - (-1)| = |8| = 8 blocks, as in choice C. This matches real-world scenarios like city blocks where you measure up or down the same street. Errors include forgetting absolute value, leading to negative distances like in D, or using incorrect operations like addition without subtraction as in A. To verify, always check if x-coordinates match for vertical distance and apply absolute value. This skill extends to monitoring distances in grids, emphasizing arithmetic with negative numbers.

This question tests identifying the quadrant of a point by examining the signs of its coordinates after plotting. Graph each point: A(3,5) in I (both positive), B(-4,2) in II (x negative, y positive), C(-3,-6) in III (both negative), D(2,-4) in IV (x positive, y negative). The point in Quadrant III is C(-3,-6), corresponding to choice D. Correct quadrant identification relies on sign rules without needing distance calculations here. Errors might involve reversing coordinates or misapplying signs, like thinking negative y means Quadrant II. To master this, plot points in all quadrants and label them. This builds understanding of the coordinate plane's structure for mapping.

This question tests graphing points in four quadrants and calculating vertical distances with same x-coordinate using absolute value. Graphing: plot (x,y) from origin, x horizontal (left negative, right positive), y vertical (down negative, up positive); distance for same x: |y₂ - y₁|. Points P(2,5) and Q(2,-3) on vertical line x=2, distance = |5 - (-3)| = |8| = 8 units, matching choice C. Correct method applies absolute value to y-difference for positive distance. Common errors: without absolute value (5 - (-3) = 8, but if reversed -8 claimed), or using x instead (|2-2|=0). Practice vertical distances with signed y-values. Absolute value critical: ensures positive distance regardless of order.

This question tests graphing points in all four quadrants and calculating horizontal distance for robot movement (|x₂-x₁| when same y). Graphing: plot ordered pair (x,y) by moving x horizontally from origin (left if negative, right if positive), then y vertically (down if negative, up if positive), marks point in appropriate quadrant (signs determine which: I both +, II x− y+, III both −, IV x+ y−). For (-8,-2) to (1,-2), same y=-2, distance |1-(-8)|=|9|=9 units, choice B correct. Absolute value ensures positive regardless of direction. Common mistakes: no | | leading to negative (e.g., -8-1=-9), or using y for horizontal. Steps: check same y, |x difference|; applications in robotics or grid navigation.

This question tests vertical distance between points sharing x-coordinate using |y₂ - y₁|. C(6,-6) and T(6,3) at x=6, distance |3 - (-6)| = |9| = 9 units, choice C. Ignores R as it's not sharing x with C or T for this calculation. Models robot paths on grids. Errors like using x-differences in D or no absolute value in B. Confirm alignment, then apply formula. Essential for coordinate-based measurements.