Math Problem Statement

1. Vocabulary: On a coordinate plane, the ordered pair (4, 4) are the ____ of a point. 2. What is the distance between points C and D on the graph? 3. Which number is halfway between -3 and 5 on the number line?

Solution

Let’s break down and solve the questions in the image step by step:


Question 1: Vocabulary

  • The ordered pair (4,4)(4, 4) represents the coordinates of a point on a coordinate plane.

Answer: coordinates


Question 2: Distance Between Points CC and DD

  • The points CC and DD are on a number line:
    • C=4C = -4
    • D=6D = 6

To find the distance between two points on a number line: Distance=DC=6(4)=6+4=10\text{Distance} = |D - C| = |6 - (-4)| = |6 + 4| = 10

Answer: 1010


Question 3: Halfway Between 3-3 and 55

  • To find the number halfway between two numbers: Midpoint=First Number+Second Number2\text{Midpoint} = \frac{\text{First Number} + \text{Second Number}}{2} Substitute: Midpoint=3+52=22=1\text{Midpoint} = \frac{-3 + 5}{2} = \frac{2}{2} = 1

Answer: C. 1


Do you have any questions or need further details? 😊

Here are 5 related questions to expand your understanding:

  1. How do you calculate the distance between two points in a 2D coordinate plane?
  2. What is the difference between the terms "coordinates" and "ordered pair"?
  3. Can you explain how absolute value plays a role in finding distance on a number line?
  4. How would you find a number one-third of the way between two given numbers on a number line?
  5. What is the formula for finding the midpoint of two points in a coordinate plane?

Tip: For midpoint or halfway questions, always add the two values and divide by 2—it works for any number line or axis.

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Math Problem Analysis

Mathematical Concepts

Coordinate geometry
Distance on a number line
Midpoint calculation

Formulas

Distance = |D - C|
Midpoint = (First Number + Second Number) / 2

Theorems

Absolute value theorem for distance
Midpoint theorem

Suitable Grade Level

Grades 6-8