To find the distance between the points [tex]\((-4,3)\)[/tex] and [tex]\((4,3)\)[/tex], we use the distance formula, which is given by:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Step-by-step:
1. Let's identify the coordinates:
- Point 1: [tex]\( (x_1, y_1) = (-4, 3) \)[/tex]
- Point 2: [tex]\( (x_2, y_2) = (4, 3) \)[/tex]
2. Substitute these coordinates into the distance formula:
[tex]\[ \text{Distance} = \sqrt{(4 - (-4))^2 + (3 - 3)^2} \][/tex]
3. Simplify inside the parentheses:
[tex]\[ \text{Distance} = \sqrt{(4 + 4)^2 + (0)^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{8^2 + 0} \][/tex]
4. Calculate [tex]\(8^2\)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
5. Now, the distance is:
[tex]\[ \text{Distance} = \sqrt{64} \][/tex]
6. Finally, calculate the square root of 64:
[tex]\[ \sqrt{64} = 8 \][/tex]
Therefore, the distance between the points [tex]\((-4, 3)\)[/tex] and [tex]\((4, 3)\)[/tex] is [tex]\(8\)[/tex] units.
The correct answer is:
A) 8 units
