Coordinate Geometry

Answer

Step 1: The points lie on the X-axis, so use distance = |x2 - x1|. Step 2: distance = |6 - 2|. Step 3: distance = |4| = 4 units. Answer: 4 units.

Answer

Step 1: The points lie on the Y-axis, so use distance = |y2 - y1|. Step 2: distance = |7 - 2|. Step 3: distance = 5 units. Answer: 5 units.

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Step 1: The points are on the X-axis. Step 2: distance = |x2 - x1| = |(-6) - (-2)|. Step 3: distance = |-4| = 4 units. Answer: 4 units. Check: Distance is never negative, so the absolute value is nece…

Answer

Distance represents length, and length cannot be negative. Example: (-6) - (-2) = -4, but distance is taken as |-4| = 4. So the absolute value is used whenever distance is found.

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Formula: distance = |x2 - x1| Here x1 and x2 are the x-coordinates of two points on the X-axis. Quick example: between (2, 0) and (8, 0), distance = |8 - 2| = 6 units.

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Formula: distance = |y2 - y1| Here y1 and y2 are the y-coordinates of two points on the Y-axis. Quick example: between (0, 3) and (0, 10), distance = |10 - 3| = 7 units.

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Step 1: Draw the right triangle using the axes. Step 2: Use Pythagorean theorem. Step 3: AB^2 = 4^2 + 3^2 = 16 + 9 = 25. Step 4: AB = sqrt(25) = 5 units. Answer: 5 units.

Answer

Step 1: Use distance from origin = sqrt(x^2 + y^2). Step 2: Substitute x = 7, y = 4. Step 3: distance = sqrt(7^2 + 4^2) = sqrt(49 + 16) = sqrt(65). Answer: sqrt(65) units.