Question

which value of x will make ab perpendicular to cd? a) 6 b) 9 c) 11 d) 13

Explanation:

Step1: Recall perpendicular - angle property

If $\overrightarrow{AB}\perp\overrightarrow{CD}$, then the angle formed at their intersection is $90^{\circ}$. So, $(7x - 11)+(5x - 7)=90$.

Step2: Combine like - terms

$(7x+5x)+(-11 - 7)=90$, which simplifies to $12x-18 = 90$.

Step3: Add 18 to both sides

$12x-18 + 18=90 + 18$, resulting in $12x=108$.

Step4: Solve for x

Divide both sides by 12: $\frac{12x}{12}=\frac{108}{12}$, so $x = 9$.

Answer:

B. 9