To find the distance between the points [tex]\((-3, 4)\)[/tex] and [tex]\((4, 4)\)[/tex] on the coordinate plane, you can use the distance formula. The distance formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let's apply this formula step-by-step for the points [tex]\((-3, 4)\)[/tex] and [tex]\((4, 4)\)[/tex]:
1. Identify the coordinates:
- [tex]\((x_1, y_1) = (-3, 4)\)[/tex]
- [tex]\((x_2, y_2) = (4, 4)\)[/tex]
2. Substitute the coordinates into the distance formula:
[tex]\[
d = \sqrt{(4 - (-3))^2 + (4 - 4)^2}
\][/tex]
3. Simplify inside the square root:
[tex]\[
d = \sqrt{(4 + 3)^2 + (0)^2}
\][/tex]
[tex]\[
d = \sqrt{7^2}
\][/tex]
[tex]\[
d = \sqrt{49}
\][/tex]
[tex]\[
d = 7
\][/tex]
So, the distance between the points [tex]\((-3, 4)\)[/tex] and [tex]\((4, 4)\)[/tex] is [tex]\(7\)[/tex] units.
