Question

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what is the distance between point p and point q? 7 units distance is always positive or 0. absolute value is always positive or 0. you can use absolute value to write an expression for the distance. which expression represents the distance between point p and point q? $|-3| + |2|$ $|4| - |3|$ $|4| + |-3|$ $|4| - |2|$ (with image of coordinate grid showing p(2,4) and q(2,-3))

Explanation:

Step1: Identify coordinates of P and Q

Point \( P \) is \( (2, 4) \), point \( Q \) is \( (2, -3) \). Since x - coordinates are same, distance is vertical.

Step2: Find vertical distance using absolute values

Vertical distance is difference in y - coordinates. So distance \( = |4 - (-3)|=|4|+|-3| \) (because \( |a - b|=|a|+|b| \) when \( b \) is negative, as \( 4-(-3)=4 + 3 \) and \( |4|+|-3|=4 + 3 \)).

Answer:

\(|4|+|-3|\)