Question

ii. for each problem, create an image using the given direction. (2 points each)
11 - 12. translate the shape 6 units right
13 - 14. reflect the shape across y - axis
iii. choose the best answer. (show your solution)

1. in triangle abc, d is the mid - point of ab and e is the mid - point of bc. if ac = 3x - 15 and de = 6, what is the value of x? a. 6 b. 7 c. 9 d. 12

Explanation:

Step1: Recall the mid - point theorem

In a triangle, if \(D\) is the mid - point of \(AB\) and \(E\) is the mid - point of \(BC\), then \(DE=\frac{1}{2}AC\) (by the mid - point theorem).

Step2: Substitute the given values into the formula

We know that \(DE = 6\) and \(AC=3x - 15\). Since \(DE=\frac{1}{2}AC\), we have the equation \(6=\frac{1}{2}(3x - 15)\).

Step3: Solve the equation for \(x\)

First, multiply both sides of the equation by \(2\): \(2\times6=3x - 15\), which simplifies to \(12 = 3x-15\).
Then, add \(15\) to both sides: \(12 + 15=3x\), so \(27 = 3x\).
Finally, divide both sides by \(3\): \(x = 9\).

Answer:

c. 9