Answer:
[tex]\sf \sqrt{218}=14.76\:\:(2\:d.p.)[/tex]
Step-by-step explanation:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the given points:
Substitute the defined points into the formula and solve for d:
[tex]\implies d=\sqrt{(3-(-4))^2+(-7-6)^2}[/tex]
[tex]\implies d=\sqrt{(7)^2+(-13)^2}[/tex]
[tex]\implies d=\sqrt{49+169}[/tex]
[tex]\implies d=\sqrt{218}[/tex]
[tex]\implies d=14.76\:\: \sf (2 \:d.p.)[/tex]
Learn more about the distance formula here:
https://brainly.com/question/28144723
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:
▪ [tex]\longrightarrow \sf{- (-4, 6) }[/tex]
▪ [tex]\longrightarrow \sf{(3, -7)}[/tex]
[tex]\leadsto[/tex] The rule of distance between the two points (x 1, y 1) and (x 2, y 2) is:
[tex]\longrightarrow \sf{d= \sqrt{ (x_2 - x_1 ) {}^{2} + (y_2 - y_1) {}^{2} } }[/tex]
▪ [tex]\longrightarrow \sf{ (x1, y1) = (-4, 6)}[/tex]
▪ [tex]\longrightarrow \sf{(x2, y2) = (3, -7)}[/tex]
[tex]\leadsto[/tex] Substitute them in the rule above:
[tex]\small\longrightarrow \sf{ d = \sqrt{(3 - 4) {}^{2} + ( - 7 - 6) {}^{2} } }[/tex]
[tex]\small\longrightarrow \sf{d= \sqrt{7 {}^{2} + ( - 13) {}^{2} } }[/tex]
[tex]\small\longrightarrow \sf{d= \sqrt{49 + 169} }[/tex]
[tex]\small\longrightarrow \sf{d= \sqrt{218} }[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\small\bm{ \small \bm{The \: \: distance \: \: between \: \: the \: \: 2 \: \: points \: \: is \: }} [/tex] [tex]\small\bm{ \: \: \sqrt{218} \: \: or \: \: 14.76.}[/tex]
