A(2,7) is a fixed point in the coordinate plane. Let B(x, 7) be any point on the same horizontal

step 1 I have a segment AB, and I know that A is at 2 -7, and B is at some number X, 7. So immediately

A(2,7) is a fixed point in the coordinate plane. Let B(x, 7)...

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Key Concepts

Distance Formula

The distance formula is a fundamental tool in coordinate geometry used to calculate the distance between two points by taking into account the differences in both the x-coordinates and y-coordinates. It is derived from the Pythagorean theorem and can be simplified in cases where points share a common coordinate value, such as on a horizontal or vertical line.

Absolute Value

The absolute value function measures the magnitude of a real number regardless of its sign. In the context of distances on the coordinate plane, the absolute value of the difference between coordinates ensures that the result is non-negative, reflecting the fact that distance cannot be negative.

Horizontal Distance

When two points lie on a horizontal line, they share the same y-coordinate, and the distance between them reduces to the absolute difference between their x-coordinates. This simplification is a direct application of the distance formula in a specific scenario where vertical displacement is zero.

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