Show that the points P(7,3), Q(6,3+root 3) and R(5,3) forms an equilateral triangle - Maths -

Question

Show that the points P(7,3), Q(6,3+root 3) and R(5,3) forms an
equilateral triangle

Duke Biswass · Accepted Answer

In an equilateral triangle all sides have the same length

so we just have to prove that in this case

points are P(7,3) , Q(6, $3 \sqrt{3}$ ) , R(5,3)

now using the formula for length between two points if A $(x_{1}, y_{1)}$ , B $(x_{2}, y_{2})$ then AB = $\sqrt{{(x_{2} - x_{1})}^{2} + (y_{2} - {y_{1})}^{2}}$

PQ = $\sqrt{{(6 - 7)}^{2} + {(3 \sqrt{3} - 3)}^{2}}$ = $\sqrt{1 + 3}$ = 2

QR = $\sqrt{{(5 - 6)}^{2} + {(3 - 3 \sqrt{3})}^{2}}$ = $\sqrt{1 + 3}$ = 2

PR = $\sqrt{{(5 - 7)}^{2} + {(3 - 3)}^{2}}$ = $\sqrt{4}$ = 2

as all sides have the same length. the triangle is equilateral

Show that the points P(7,3), Q(6,3+root 3) and R(5,3) forms an equilateral triangle.