QuestionCalculate the distance between the points $M(-2,3)$ and $N(8,2)$ . Choose from: A. 8 B. $\sqrt{61}$ C. 10 D. $\sqrt{101}$

Studdy Solution

STEP 1

Assumptions1. The coordinates of point M are (-,3) . The coordinates of point N are (8,)
3. We are using the Euclidean distance formula to find the distance between two points in a plane.

STEP 2

The Euclidean distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane is given by the formula $d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the coordinates of points M and N into the distance formula.
$d = \sqrt{(8 - (-2))^2 + (2 -3)^2}$

STEP 4

implify the expression inside the square root.
$d = \sqrt{(8 +2)^2 + (-1)^2}$

STEP 5

Perform the calculations inside the parentheses.
$d = \sqrt{10^2 +1^2}$

STEP 6

Square the numbers inside the square root.
$d = \sqrt{100 +1}$

STEP 7

Add the numbers inside the square root.
$d = \sqrt{101}$ So, the distance between points M and N is $\sqrt{101}$ .

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QuestionCalculate the distance between the points $M(-2,3)$ and $N(8,2)$ . Choose from: A. 8 B. $\sqrt{61}$ C. 10 D. $\sqrt{101}$

Studdy Solution

STEP 1

Assumptions1. The coordinates of point M are (-,3) . The coordinates of point N are (8,)
3. We are using the Euclidean distance formula to find the distance between two points in a plane.

STEP 2

The Euclidean distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane is given by the formula $d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the coordinates of points M and N into the distance formula.
$d = \sqrt{(8 - (-2))^2 + (2 -3)^2}$

STEP 4

implify the expression inside the square root.
$d = \sqrt{(8 +2)^2 + (-1)^2}$

STEP 5

Perform the calculations inside the parentheses.
$d = \sqrt{10^2 +1^2}$

STEP 6

Square the numbers inside the square root.
$d = \sqrt{100 +1}$

STEP 7

Add the numbers inside the square root.
$d = \sqrt{101}$ So, the distance between points M and N is $\sqrt{101}$ .

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QuestionCalculate the distance between the points M(−2,3)M(-2,3)M(−2,3) and N(8,2)N(8,2)N(8,2). Choose from: A. 8 B. 61\sqrt{61}61​ C. 10 D. 101\sqrt{101}101​

Studdy Solution

STEP 1

Assumptions1. The coordinates of point M are (-,3) . The coordinates of point N are (8,)3. We are using the Euclidean distance formula to find the distance between two points in a plane.

STEP 2

The Euclidean distance between two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) in a plane is given by the formulad=(x2−x1)2+(y2−y1)2d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}d=(x2−x1)2+(y2−y1)2​

STEP 3

Now, plug in the given values for the coordinates of points M and N into the distance formula.d=(8−(−2))2+(2−3)2d = \sqrt{(8 - (-2))^2 + (2 -3)^2}d=(8−(−2))2+(2−3)2​

STEP 4

implify the expression inside the square root.d=(8+2)2+(−1)2d = \sqrt{(8 +2)^2 + (-1)^2}d=(8+2)2+(−1)2​

STEP 5

Perform the calculations inside the parentheses.d=102+12d = \sqrt{10^2 +1^2}d=102+12​

STEP 6

Square the numbers inside the square root.d=100+1d = \sqrt{100 +1}d=100+1​

STEP 7

Add the numbers inside the square root.d=101d = \sqrt{101}d=101​So, the distance between points M and N is 101\sqrt{101}101​.

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QuestionCalculate the distance between the points $M(-2,3)$ and $N(8,2)$ . Choose from: A. 8 B. $\sqrt{61}$ C. 10 D. $\sqrt{101}$

Assumptions1. The coordinates of point M are (-,3) . The coordinates of point N are (8,)
3. We are using the Euclidean distance formula to find the distance between two points in a plane.

The Euclidean distance between two points $(x1, y1)$ and $(x2, y2)$ in a plane is given by the formula $d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Now, plug in the given values for the coordinates of points M and N into the distance formula.
$d = \sqrt{(8 - (-2))^2 + (2 -3)^2}$

implify the expression inside the square root.
$d = \sqrt{(8 +2)^2 + (-1)^2}$

Perform the calculations inside the parentheses.
$d = \sqrt{10^2 +1^2}$

Square the numbers inside the square root.
$d = \sqrt{100 +1}$

Add the numbers inside the square root.
$d = \sqrt{101}$ So, the distance between points M and N is $\sqrt{101}$ .