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.

k=1

Step-by-step 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)

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step-by-step explanation: