Question

what is the distance between the points (0,0) and (3,4)?
a. 3
b. 6
c. 7
d. 4

what are the coordinates of the origin on a coordinate plane?
a. (0,1)
b. (0,0)
c. (1,1)
d. (1,0)

if point a is at (2,3) and point b is at (5,7), what is the distance between point a and point b?
a. 4
b. 5
c. 6
d. 7

what is the distance between points (-2,-3) and (2,1)?
a. sqrt{16}
b. sqrt{15}
c. sqrt{32}
d. sqrt{34}

Explanation:

First Question:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(3,4)\).

Step2: Substitute values

\(d=\sqrt{(3 - 0)^2+(4 - 0)^2}=\sqrt{9 + 16}=\sqrt{25}=5\)

Second Question:

By the definition of the origin in a coordinate plane, it is the point where the \(x\) - axis and \(y\) - axis intersect, and its coordinates are \((0,0)\)

Third Question:

Step1: Apply the distance formula

For points \(A(2,3)\) and \(B(5,7)\), using \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \(x_1 = 2,y_1=3,x_2 = 5,y_2 = 7\)

Step2: Calculate

\(d=\sqrt{(5 - 2)^2+(7 - 3)^2}=\sqrt{9+16}=\sqrt{25 + 11}=\sqrt{36}=6\)

Fourth Question:

Step1: Use the distance formula

For points \((-2,-3)\) and \((2,1)\), \(d=\sqrt{(2-(-2))^2+(1-(-3))^2}\)

Step2: Simplify

\(d=\sqrt{(2 + 2)^2+(1 + 3)^2}=\sqrt{16+16}=\sqrt{32}\)

Answer:

1. First Question:

• A. \(5\)

1. Second Question:

• B. \((0,0)\)

1. Third Question:

• C. \(6\)

1. Fourth Question:

• C. \(\sqrt{32}\)