Question

find the distance between the points (-4, -5) and (6, -5).

Explanation:

Step1: Identify y - coordinates

Both points \((-4, -5)\) and \((6, -5)\) have the same \(y\) - coordinate (\(y=-5\)). So, the line segment joining them is horizontal.

Step2: Use distance formula for horizontal line

For two points \((x_1,y)\) and \((x_2,y)\) (since \(y\) - coordinates are equal), the distance \(d\) between them is given by \(d=\vert x_2 - x_1\vert\).
Here, \(x_1=-4\) and \(x_2 = 6\).
So, \(d=\vert6-(-4)\vert=\vert6 + 4\vert=\vert10\vert = 10\).

Answer:

10