Question

1. (-6.1, -8.4) and (-6.1, -4.2)
2. (-5.4, 4.7) and (0.6, 4.7)

Explanation:

Step1: Identify the formula for distance when \(x\)-coordinates are same

When two points \((x_1,y_1)\) and \((x_2,y_2)\) have \(x_1 = x_2\), the distance \(d=\vert y_1 - y_2\vert\).
For the points \((-6.1,-8.4)\) and \((-6.1,-4.2)\), \(x_1=-6.1,x_2 = -6.1,y_1=-8.4,y_2=-4.2\).
\(d=\vert-8.4-(-4.2)\vert\)

Step2: Simplify the expression

\(\vert-8.4 + 4.2\vert=\vert-4.2\vert = 4.2\)

Step3: For the points \((-5.4,4.7)\) and \((0.6,4.7)\)

When two points \((x_1,y_1)\) and \((x_2,y_2)\) have \(y_1 = y_2\), the distance \(d=\vert x_1 - x_2\vert\). Here \(x_1=-5.4,x_2 = 0.6,y_1 = 4.7,y_2=4.7\)
\(d=\vert-5.4 - 0.6\vert\)

Step4: Simplify the expression

\(\vert-6\vert=6\)

Answer:

For the points \((-6.1,-8.4)\) and \((-6.1,-4.2)\), the distance is \(4.2\) units.
For the points \((-5.4,4.7)\) and \((0.6,4.7)\), the distance is \(6\) units.