Question

- (-4, 6) and (3, -7) find the distance between the two points

Answer 1

Answer:

$\sf \sqrt{218}=14.76\:\:(2\:d.p.)$

Step-by-step explanation:

Distance between two points

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}$

Define the given points:

• $(x_1,y_1)=(-4,6)$

• $(x_2,y_2)=(3,-7)$

Substitute the defined points into the formula and solve for d:

$\implies d=\sqrt{(3-(-4))^2+(-7-6)^2}$

$\implies d=\sqrt{(7)^2+(-13)^2}$

$\implies d=\sqrt{49+169}$

$\implies d=\sqrt{218}$

$\implies d=14.76\:\: \sf (2 \:d.p.)$

Learn more about the distance formula here:

brainly.com/question/28144723

Answer 2

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

Given:

▪ $\longrightarrow \sf{- (-4, 6) }$

▪ $\longrightarrow \sf{(3, -7)}$

$\leadsto$ The rule of distance between the two points (x 1, y 1) and (x 2, y 2) is:

$\longrightarrow \sf{d= \sqrt{ (x_2 - x_1 ) {}^{2} + (y_2 - y_1) {}^{2} } }$

▪ $\longrightarrow \sf{ (x1, y1) = (-4, 6)}$

▪ $\longrightarrow \sf{(x2, y2) = (3, -7)}$

$\leadsto$ Substitute them in the rule above:

$\small\longrightarrow \sf{ d = \sqrt{(3 - 4) {}^{2} + ( - 7 - 6) {}^{2} } }$

$\small\longrightarrow \sf{d= \sqrt{7 {}^{2} + ( - 13) {}^{2} } }$

$\small\longrightarrow \sf{d= \sqrt{49 + 169} }$

$\small\longrightarrow \sf{d= \sqrt{218} }$

$\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}$

$\small\bm{ \small \bm{The \: \: distance \: \: between \: \: the \: \: 2 \: \: points \: \: is \: }}$ $\small\bm{ \: \: \sqrt{218} \: \: or \: \: 14.76.}$