To find the distance between the points [tex]\((-4, 7)\)[/tex] and [tex]\((-4, -10)\)[/tex], you can use the distance formula for two points in a coordinate plane. The general distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Step-by-step solution:
1. Identify the coordinates of the two points:
- Point 1: [tex]\((-4, 7)\)[/tex]
- Point 2: [tex]\((-4, -10)\)[/tex]
2. Plug the coordinates into the distance formula:
[tex]\[ \text{Distance} = \sqrt{((-4) - (-4))^2 + ((-10) - 7)^2} \][/tex]
3. Simplify the expressions inside the square root:
[tex]\[ \text{Distance} = \sqrt{(0)^2 + (-10 - 7)^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{0 + (-17)^2} \][/tex]
4. Calculate the square of [tex]\(-17\)[/tex]:
[tex]\[ \text{Distance} = \sqrt{0 + 289} \][/tex]
5. Simplify the square root:
[tex]\[ \text{Distance} = \sqrt{289} \][/tex]
[tex]\[ \text{Distance} = 17 \][/tex]
Therefore, the distance between the points [tex]\((-4, 7)\)[/tex] and [tex]\((-4, -10)\)[/tex] is 17 units. The correct answer is:
[tex]\[ 17 \text{ units} \][/tex]
