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Objective 1: Apply the midpoint and distance formulas on a coordinate plane
1. Point A is at (-2,4) and Point B is at (7,-3)
a. Find the distance between the two points
(-2,4)
(7,-3)-



Answer :

GinnyAnswer
Certainly! Let's find the distance between the two points A and B using the distance formula.

Points:
- Point A: [tex]\((-2, 4)\)[/tex]
- Point B: [tex]\((7, -3)\)[/tex]

Distance Formula:
The distance [tex]\( d \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] on a coordinate plane is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Step-by-Step Solution:

1. Identify the coordinates:
- Point A: [tex]\((x_1, y_1) = (-2, 4)\)[/tex]
- Point B: [tex]\((x_2, y_2) = (7, -3)\)[/tex]

2. Subtract the x-coordinates:
[tex]\[ x_2 - x_1 = 7 - (-2) = 7 + 2 = 9 \][/tex]

3. Subtract the y-coordinates:
[tex]\[ y_2 - y_1 = -3 - 4 = -7 \][/tex]

4. Square the differences:
[tex]\[ (x_2 - x_1)^2 = 9^2 = 81 \][/tex]
[tex]\[ (y_2 - y_1)^2 = (-7)^2 = 49 \][/tex]

5. Add the squared differences:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 81 + 49 = 130 \][/tex]

6. Take the square root of the sum:
[tex]\[ d = \sqrt{130} \approx 11.40175425099138 \][/tex]

Therefore, the distance between point A [tex]\((-2, 4)\)[/tex] and point B [tex]\((7, -3)\)[/tex] is approximately [tex]\(11.40175425099138\)[/tex].

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