Question

What is the distance between (–3,1) and (2,4) on the coordinate plane?

Answer 1

try this formula distance =

$\sqrt{(x2 - x1} + \sqrt{(y2 - y1)}$

Answer 2

Answer:

$\Large\boxed{\mathsf{\sqrt{34}}}}$

Step-by-step explanation:

TO FIND:

The distance between (-3, 1) and (2, 4) on the coordinate plane.

DISTANCE FORMULA:

$\displaystyle \mathsf{\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}}}}$

SOLUTIONS:

Distance between the (-3, 1) and (2, 4).

$\displaystyle \mathsf{\sqrt{(2-(-3))^2+(4-1)^2}}$

$\displaystyle \mathsf{\sqrt{\left(2+3\right)^2+\left(4-1\right)^2}}}}$

Add.

$\displaystyle \mathsf{2+3=5}$

$\displaystyle \mathsf{\sqrt{5^2+(4-1)^2}}$

Subtract.

$\displaystyle \mathsf{4-1=3}$

$\displaystyle \mathsf{\sqrt{5^2+3^2}}}}$

Solve by exponent.

$\displaystyle \mathsf{5^2=5\times5=25}$

$\displaystyle \mathsf{\sqrt{25+3^2}}}}$

$\displaystyle \mathsf{3^2=3\times3=9}$

$\displaystyle \mathsf{\sqrt{25+9}}$

Add.

$\displaystyle \mathsf{25+9=\boxed{\mathsf{34}}}}$

$\Large\boxed{\mathsf{\Rightarrow \sqrt{34}}}}}$

The distance between of (-3,1) and (2,4) is 34.