Question

How far from the origin is the point (-5, -12)?

Answer 1

the origin is (0,0)

so it is 5 units left from orogin and 12 units down
if we were to start from the origin, and draw a line that is 5 units long to the left, then draw a line that is 12 units down from that point, then connect the end point to the origin we get a triangle

legs are legnth 12 and 5
hypotonuse=?
12^2+5^2=?^2
144+25=?^2
169=?^2
sqrt both sides
13=?

answer is 13 units

or use distance fomrula
which is overkill
distance between ponts (x1,y1) and (x2,y2) is
D=
`\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}`
in this case, between (0,0) and (-5,-12)
D=
`\sqrt{(-5-0)^(2)+(-12-0)^(2)}`
D=
`\sqrt{(-5)^(2)+(-12)^(2)}`
D=
`√(25+144)`
D=
`√(169)`
D=13


asnswer is 13 units (distance is always positive)

Answer 2

To get to the origin from (-5, -12)
You move 5 to the right, and 12 up.
Since the numbers are a negative, they turn into a positive to convert to the middle (0, 0)