Question

statements reasons 1. r ∥ s given 2. $m_r = \frac{d - b}{c - 0} = \frac{d - b}{c}$ $m_s = \frac{0 - a}{c - 0} = -\frac{a}{c}$ application of the slope formula 3. distance from (0, b) to (0, a) equals the distance from (c, d) to (c, 0) definition of parallel lines 4. ? application of the distance formula 5. $m_r = \frac{(b - a) - b}{c}$ substitution property of equality 6. $m_r = -\frac{a}{c}$ inverse property of addition 7. $m_r = m_s$ substitution property of equality the table and corresponding image show the proof of the relationship between the slopes of two parallel lines. what is the missing statement in step 4? a. $d - 0 = b - a$ b. $b - c = d - a$ c. $c - d = b - a$ d. $c - 0 = a - b$

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\vert y_2 - y_1\vert\) when \(x_1 = x_2\) (vertical distance) or \(d=\vert x_2 - x_1\vert\) when \(y_1 = y_2\) (horizontal distance).
For the points \((0,b)\) and \((0,a)\) (same \(x -\)coordinate), the distance is \(\vert a - b\vert=b - a\) (assuming \(b\gt a\)).
For the points \((c,d)\) and \((c,0)\) (same \(x -\)coordinate), the distance is \(\vert d - 0\vert=d\).

Step2: Use the given relationship

Since the distance from \((0,b)\) to \((0,a)\) equals the distance from \((c,d)\) to \((c,0)\), we have \(d-0=b - a\).

Answer:

A. \(d - 0=b - a\)