Question

w x z y
←┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼→
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
○ true
● false

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

p q
←┼──┼──┼──┼──┼──┼──┼──┼──┼──┼──┼→
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Explanation:

Step1: Find coordinates of P and Q

From the number line, \( P = -5 \), \( Q = 7 \).

Step2: Use section formula

The formula for a point \( X \) that divides the line segment joining \( P(x_1) \) and \( Q(x_2) \) in the ratio \( m:n \) (here \( m = 3 \), \( n = 1 \) as it's \( \frac{3}{4} \) distance from \( P \) to \( Q \)) is \( X = x_1+\frac{m}{m + n}(x_2 - x_1) \).

Substitute \( x_1=-5 \), \( x_2 = 7 \), \( m = 3 \), \( n = 1 \):

\( X=-5+\frac{3}{3 + 1}(7-(-5)) \)

Step3: Simplify the expression

First, calculate \( 7-(-5)=12 \).

Then, \( \frac{3}{4}\times12 = 9 \).

Now, \( -5 + 9 = 4 \).

Answer:

\( 4 \)