find the distance from the orgin to each of the following points .If your answer is irrational,leave it in radical form.
a.(3,-7)
b.(-4,6)
c.(0,5)
d.(6,0)
e.(-2,-4)
f.(0,0)
my answers : what do they mean by leave it radical form
a.sqrt 58
b.Sqrt 52 = 2sqrt 13 or should i just leave it 52
c.5
d.6
e.i don't know ?? is it 2 sqrt5 or should i just leave it 20
f.0
Leave in radical form means don't simplify the sqrt (radical) to exact value.
Example, exact value of (sqrt(2))= 1.4142
All your answers are correct.
Always simplify radicals, ie,(like you did), but wasn't sure,
(sqrt(52)) = 2(sqrt(13)) don't leave as
(sqrt(52))
(sqrt(20) = 2(sqrt(5)) don't leave as
(sqrt(20)
The term "leave it in radical form" means that you should express the answer as a square root, without simplifying it any further.
a. To find the distance from the origin (0,0) to the point (3,-7), you can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((3 - 0)^2 + (-7 - 0)^2)
Distance = sqrt(3^2 + (-7)^2)
Distance = sqrt(9 + 49)
Distance = sqrt(58)
So the distance from the origin to point (3,-7) is sqrt(58).
b. To find the distance from the origin to the point (-4,6), you can use the distance formula again:
Distance = sqrt((-4 - 0)^2 + (6 - 0)^2)
Distance = sqrt((-4)^2 + 6^2)
Distance = sqrt(16 + 36)
Distance = sqrt(52)
So the distance from the origin to point (-4,6) is sqrt(52) or you could also write it as 2sqrt(13).
c. The point (0,5) lies on the y-axis, so the distance from the origin (0,0) to this point is simply the y-coordinate, which is 5.
So the distance from the origin to point (0,5) is 5.
d. The point (6,0) lies on the x-axis, so the distance from the origin (0,0) to this point is simply the x-coordinate, which is 6.
So the distance from the origin to point (6,0) is 6.
e. To find the distance from the origin to the point (-2,-4), you can use the distance formula:
Distance = sqrt((-2 - 0)^2 + (-4 - 0)^2)
Distance = sqrt((-2)^2 + (-4)^2)
Distance = sqrt(4 + 16)
Distance = sqrt(20)
So the distance from the origin to the point (-2,-4) is sqrt(20) or you could also write it as 2sqrt(5).
f. The point (0,0) is the origin, so the distance from the origin to itself is 0.
So the distance from the origin to the point (0,0) is 0.
To find the distance from the origin to each point, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance for each point:
a. (3, -7)
Using the distance formula:
d = sqrt((3 - 0)^2 + (-7 - 0)^2)
d = sqrt(9 + 49)
d = sqrt(58)
To leave it in radical form means representing the answer as an exact expression without approximating it to a decimal. Therefore, the answer for point a is sqrt(58).
b. (-4, 6)
Using the distance formula:
d = sqrt((-4 - 0)^2 + (6 - 0)^2)
d = sqrt(16 + 36)
d = sqrt(52)
You can simplify sqrt(52) to 2sqrt(13), where sqrt(13) cannot be simplified further. So, the answer for point b is 2sqrt(13).
c. (0, 5)
Using the distance formula:
d = sqrt((0 - 0)^2 + (5 - 0)^2)
d = sqrt(0 + 25)
d = sqrt(25)
d = 5
Since 5 is a rational number, you don't need to leave it in radical form. The answer for point c is 5.
d. (6, 0)
Using the distance formula:
d = sqrt((6 - 0)^2 + (0 - 0)^2)
d = sqrt(36 + 0)
d = sqrt(36)
d = 6
Again, since 6 is a rational number, you don't need to leave it in radical form. The answer for point d is 6.
e. (-2, -4)
Using the distance formula:
d = sqrt((-2 - 0)^2 + (-4 - 0)^2)
d = sqrt(4 + 16)
d = sqrt(20)
You can simplify sqrt(20) to 2sqrt(5), where sqrt(5) cannot be simplified further. Thus, the answer for point e is 2sqrt(5).
f. (0, 0)
The distance from the origin to itself is always 0, since you're already at the origin. Therefore, the answer for point f is 0.