Plot the points [tex]\((-3,4)\)[/tex] and [tex]\((4,4)\)[/tex] on the coordinate plane below.

What is the distance between these two points?

[tex]\(\square\)[/tex] units



Answer :

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.