Question

1. find the distance between the two points: t(6,17) and d(6,24)

a. 41
b. 7
c. 10
d. 9

1. if t is the mid - point of su, what is the measure of st?

a. 11
b. 77
c. 3
d. 21

Explanation:

Step1: Calculate the distance between \(T(6,17)\) and \(D(6,24)\)

Since the \(x -\)coordinates are the same (\(x_1 = x_2=6\)), use the formula \(d=\vert y_2 - y_1\vert\). Here \(y_1 = 17\) and \(y_2 = 24\), so \(d=\vert24 - 17\vert\).

Step2: Simplify the expression

\(\vert24 - 17\vert=\vert7\vert = 7\)

Step3: Solve for \(x\) when \(T\) is the mid - point of \(SU\)

If \(T\) is the mid - point of \(SU\), then \(ST=TU\). So \(7x=4x + 33\). Subtract \(4x\) from both sides: \(7x-4x=4x + 33-4x\), which gives \(3x=33\). Divide both sides by \(3\): \(x = 11\).

Step4: Calculate the length of \(ST\)

Substitute \(x = 11\) into \(ST = 7x\). So \(ST=7\times11=77\)

Answer:

1. B. 7
2. B. 77