Question

1. true or false: $overline{xy} cong overline{wz}$

(number line with points w at -5, x at -1, z at 4, y at 7; options: true, false)

1. the coordinate of point x on $overline{pq}$ that is $\frac{3}{4}$ of the distance from p to q is ______.

(number line with points p at -5, q at 7)

Explanation:

Problem 5

To determine if \(\overline{XY} \cong \overline{WZ}\), we calculate the lengths of both segments. For \(\overline{XY}\), the coordinates of \(X\) is \(-1\) and \(Y\) is \(7\), so length \(XY = |7 - (-1)| = 8\). For \(\overline{WZ}\), the coordinates of \(W\) is \(-5\) and \(Z\) is \(4\), so length \(WZ = |4 - (-5)| = 9\). Since \(8
eq9\), the segments are not congruent.

Step1: Find coordinates of P and Q

From the number line, \(P\) is at \(-5\) and \(Q\) is at \(7\).

Step2: Use section formula

The formula for a point \(X\) that divides the segment \(PQ\) in the ratio \(m:n\) (here \(m = 3\), \(n = 1\) as it's \(\frac{3}{4}\) from \(P\) to \(Q\)) is \(x=\frac{mx_Q+nx_P}{m + n}\). Substituting \(m = 3\), \(n = 1\), \(x_P=-5\), \(x_Q = 7\):
\[x=\frac{3\times7+1\times(-5)}{3 + 1}=\frac{21-5}{4}=\frac{16}{4}=4\]

Answer:

False

Problem 6