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Calculate horizontal and vertical distances between points

Horizontal distance measures the change in the xx-coordinates, and vertical distance measures the change in the yy-coordinates; each is found as the absolute difference of the corresponding coordinates, in coordinate units. This applies to points sharing a coordinate or to the horizontal and vertical components between any two plotted points, including negative coordinates, and distinguishes component distances from diagonal distance, which is addressed separately through the Pythagorean relationship.

Detailed Explanation: Calculate horizontal and vertical distances between points

To find the horizontal distance between two points, compare their xx-coordinates:

horizontal distance=∣x2−x1∣\text{horizontal distance}= \vert x_2-x_1 \vert

To find the vertical distance, compare their yy-coordinates:

vertical distance=∣y2−y1∣\text{vertical distance}= \vert y_2-y_1 \vert

The absolute value makes the distance positive, no matter which point comes first.

Example: Find the horizontal and vertical distances between A(−3,2)A(-3,2) and B(4,−5)B(4,-5).

  1. Find the horizontal distance by using the xx-coordinates, −3-3 and 44:

∣4−(−3)∣=∣4+3∣=7 \vert 4-(-3) \vert = \vert 4+3 \vert =7

The horizontal distance is 77 coordinate units.

  1. Find the vertical distance by using the yy-coordinates, 22 and −5-5:

∣−5−2∣=∣−7∣=7 \vert -5-2 \vert = \vert -7 \vert =7

The vertical distance is 77 coordinate units.

So, the points are 77 units apart horizontally and 77 units apart vertically. These are the horizontal and vertical components; they are not the diagonal distance between the points.

Learn by doing: Calculate horizontal and vertical distances between points

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    Cartesian Grid - Distance Between Points (Straight)

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