Question

The diagram on the right shows an isosceles triangle

EFG with vertices E(0,k), F(4,4) and G(7,8). EF
and FG have the same length.
(a) Find the value of k.

Answer 1

k=1

Explanation:

so FG and FE are equal meaning same magnitude

formula for magnitude is √{x2-x1}+{y2-y1}

(the square root is for all of it)

so use line FG since you have both points

you get √7 as magnitude

then apply it to FE

√7=√(4-0)+(4-k)

you can square both sides to remove the root and you get k=1

(when calculating magnitude the value is always absolute no regard to signs)