Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Questions:

(a) [tex]O(2,2)[/tex], [tex]A(5,4)[/tex], and [tex]B(-1,4)[/tex] are three points. Show that [tex]OA = OB[/tex].

Sagot :

GinnyAnswer
Certainly! Let's solve the problem step-by-step to demonstrate that the distance between point [tex]\(O(2, 2)\)[/tex] and point [tex]\(A(5, 4)\)[/tex] is equal to the distance between point [tex]\(O(2, 2)\)[/tex] and point [tex]\(B(-1, 4)\)[/tex].

### Step-by-Step Solution:

#### (a) Calculate the distance [tex]\(OA\)[/tex] between points [tex]\(O\)[/tex] and [tex]\(A\)[/tex]:

Points:
[tex]\( O = (2, 2) \)[/tex]
[tex]\( A = (5, 4) \)[/tex]

The 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]

Using the coordinates of [tex]\(O\)[/tex] and [tex]\(A\)[/tex]:
[tex]\[ OA = \sqrt{(5 - 2)^2 + (4 - 2)^2} \][/tex]

Calculate the differences:
[tex]\[ x\text{-difference} = 5 - 2 = 3 \][/tex]
[tex]\[ y\text{-difference} = 4 - 2 = 2 \][/tex]

Square these differences:
[tex]\[ x\text{-difference squared} = 3^2 = 9 \][/tex]
[tex]\[ y\text{-difference squared} = 2^2 = 4 \][/tex]

Add these squares and take the square root:
[tex]\[ OA = \sqrt{9 + 4} = \sqrt{13} \approx 3.605551275463989 \][/tex]

#### (b) Calculate the distance [tex]\(OB\)[/tex] between points [tex]\(O\)[/tex] and [tex]\(B\)[/tex]:

Points:
[tex]\( O = (2, 2) \)[/tex]
[tex]\( B = (-1, 4) \)[/tex]

Using the coordinates of [tex]\(O\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[ OB = \sqrt{(-1 - 2)^2 + (4 - 2)^2} \][/tex]

Calculate the differences:
[tex]\[ x\text{-difference} = -1 - 2 = -3 \][/tex]
[tex]\[ y\text{-difference} = 4 - 2 = 2 \][/tex]

Square these differences:
[tex]\[ x\text{-difference squared} = (-3)^2 = 9 \][/tex]
[tex]\[ y\text{-difference squared} = 2^2 = 4 \][/tex]

Add these squares and take the square root:
[tex]\[ OB = \sqrt{9 + 4} = \sqrt{13} \approx 3.605551275463989 \][/tex]

#### (c) Compare the distances [tex]\(OA\)[/tex] and [tex]\(OB\)[/tex]:

We have:
[tex]\[ OA \approx 3.605551275463989 \][/tex]
[tex]\[ OB \approx 3.605551275463989 \][/tex]

Therefore, we can conclude:
[tex]\[ OA = OB \][/tex]

Hence, the distances from point [tex]\(O\)[/tex] to points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are equal.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.