Question

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what is the distance between point f and the origin? 8 units. what is the distance between point g and the origin? 2 units. what is true about the points coordinates and their distances from the origin? the distance from each point to the origin is equal to its ? dropdown. (graph: coordinate plane with f(0,8) and g(0,2))

Explanation:

For a point \((x,y)\) on the coordinate plane, the distance from the origin \((0,0)\) can be calculated using the distance formula \(d = \sqrt{(x - 0)^2+(y - 0)^2}=\sqrt{x^{2}+y^{2}}\). For points \(F(0,8)\) and \(G(0,2)\), the \(x\)-coordinate is \(0\). So the distance formula simplifies to \(d=\sqrt{0^{2}+y^{2}}=\vert y\vert\). Since \(y\) is non - negative in these cases ( \(y = 8\) for \(F\) and \(y=2\) for \(G\)), the distance from each point to the origin is equal to its \(y\) - coordinate.

Answer:

\(y\) - coordinate