Find the distance between points M(−3, 8) and N(5, −7) and select the correct option.

Question

ScanSolve AI Tutor · Accepted Answer

To find the distance between two points M and N, we use the distance formula.

Identify the coordinates of points M and N.
Given points are $M(-3, 8)$ and $N(5, -7)$ .
Let $(x_1, y_1) = (-3, 8)$ and $(x_2, y_2) = (5, -7)$ .
Apply the distance formula.
The distance formula is given by:
$MN = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute the coordinates into the formula.
$MN = \sqrt{(5 - (-3))^2 + (-7 - 8)^2}$
Simplify the terms inside the parentheses.
$MN = \sqrt{(5 + 3)^2 + (-15)^2}$ $MN = \sqrt{(8)^2 + (-15)^2}$
Square the terms.
$MN = \sqrt{64 + 225}$
Add the squared terms.
$MN = \sqrt{289}$
Calculate the square root.
$MN = 17$
The distance MN is 17 units.

Comparing this with the given options:

(a) 8 units

(b) 11 units

(c) 15 units

(d) 17 units

The correct option is (d).

The final answer is $\boxed{\text{17 units}}$ .

Find the distance between points M(-3, 8) and N(5, -7) and select the correct option.