Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Find reliable solutions to your questions quickly and easily with help from our experienced experts.
Sagot :
To find the distance between the points [tex]\((4, 6)\)[/tex] and [tex]\((7, -3)\)[/tex], we use the distance formula, which is defined as:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, [tex]\((x_1, y_1) = (4, 6)\)[/tex] and [tex]\((x_2, y_2) = (7, -3)\)[/tex].
Let's proceed step-by-step:
1. Calculate the difference in the [tex]\(x\)[/tex]-coordinates:
[tex]\[ x_2 - x_1 = 7 - 4 = 3 \][/tex]
Then square this difference:
[tex]\[ (x_2 - x_1)^2 = 3^2 = 9 \][/tex]
2. Calculate the difference in the [tex]\(y\)[/tex]-coordinates:
[tex]\[ y_2 - y_1 = -3 - 6 = -9 \][/tex]
Then square this difference:
[tex]\[ (y_2 - y_1)^2 = (-9)^2 = 81 \][/tex]
3. Sum these squared differences:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 9 + 81 = 90 \][/tex]
4. Take the square root of the sum to get the distance:
[tex]\[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{90} \approx 9.4868 \][/tex]
Given the provided multiple-choice options, the correct expression that matches our calculations and gives the distance is:
[tex]\[ \text{Option B: } \sqrt{(4-7)^2 + (6+3)^2} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\sqrt{(4-7)^2 + (6+3)^2}} \][/tex]
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, [tex]\((x_1, y_1) = (4, 6)\)[/tex] and [tex]\((x_2, y_2) = (7, -3)\)[/tex].
Let's proceed step-by-step:
1. Calculate the difference in the [tex]\(x\)[/tex]-coordinates:
[tex]\[ x_2 - x_1 = 7 - 4 = 3 \][/tex]
Then square this difference:
[tex]\[ (x_2 - x_1)^2 = 3^2 = 9 \][/tex]
2. Calculate the difference in the [tex]\(y\)[/tex]-coordinates:
[tex]\[ y_2 - y_1 = -3 - 6 = -9 \][/tex]
Then square this difference:
[tex]\[ (y_2 - y_1)^2 = (-9)^2 = 81 \][/tex]
3. Sum these squared differences:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 9 + 81 = 90 \][/tex]
4. Take the square root of the sum to get the distance:
[tex]\[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{90} \approx 9.4868 \][/tex]
Given the provided multiple-choice options, the correct expression that matches our calculations and gives the distance is:
[tex]\[ \text{Option B: } \sqrt{(4-7)^2 + (6+3)^2} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{\sqrt{(4-7)^2 + (6+3)^2}} \][/tex]
Answer:
B. \(√((4-7)^2 + (6+3)^2)\)
Step-by-step explanation:
To find the distance between two points we use the distance formula:
sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)
sqrt( ( 4-7) ^2 + ( (6--3) ^2)
sqrt( ( 4-7) ^2 + ( (6+3) ^2)
√((4-7)^2 + (6+3)^2)
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.