Find the co-ordinates of a point on the y-axis which is equidistant from (9-3,5) and (2,3).
What formula do I use to find these co-ordinates?
please and thank you
You appear to have a typo in (9-3,5)
In any case, find the equation of the right-bisector of the line joining the two given points.
(find the midpoint, and the slope of the line through the two given points, the slope of the perpendicular is the negative reciprocal of the above slope.
Once you have the line, let x=0 to find the y-intercept.)
(9-3,5) is suppose to be (-3,5)
midpoint:
((-3+2)/2,(5+3)/2)
=(-1/2,4)
correct???
slope:
m=(3-5)/(2-(-3))
m=-2/5
correct???
perpendicular slope:
m=5/2
correct???
y=(-2/5)x+b
5=(-2/5)(-3)+b
5=6/5+b
5-6/5=b
19/5=b
correct??? It doesn't look right to me but I'm not sure.
please and thank you
P=(-3,5)
Q=(2,3)
midpoint M=(-1/2,4)
slope of PQ = (3-5)/((2-(-3)) = -2/5
slope of perpendicular is 5/2
Now you have a point M=(-1/2,4) and a slope m=5/2
so far, so good. Now, you messed up by using the slope of PQ, rather than the perpendicular bisector. (and after having gone to all the trouble of finding its slope!)
using the point-slope form of the line:
y-4 = 5/2(x+1/2) = 5/2 x + 5/4
y = 5/2 x + 21/4
y-intercept is 21/4
thank you
To find the coordinates of a point on the y-axis that is equidistant from two given points, you can follow these steps:
1. First, let's identify the two given points:
Point A: (9,5)
Point B: (2,3)
2. Since we are looking for a point on the y-axis, we know that the x-coordinate of this point will be 0. So, the unknown point can be represented as (0, y).
3. Now, we need to find the y-coordinate. We'll use the distance formula to equate the distances from the unknown point to points A and B:
Distance from (0, y) to A = Distance from (0, y) to B
Applying the distance formula, we have:
√((x₂ - x₁)² + (y₂ - y₁)²) = √((x₃ - x₁)² + (y₃ - y₁)²)
Substituting the values of the given points:
√((0 - 9)² + (y - 5)²) = √((0 - 2)² + (y - 3)²)
4. Simplifying the equation, we will square both sides to eliminate the square roots:
(0 - 9)² + (y - 5)² = (0 - 2)² + (y - 3)²
81 + (y - 5)² = 4 + (y - 3)²
5. Expanding and rearranging the equation, we get:
(y - 5)² - (y - 3)² = 4 - 81
y² - 10y + 25 - y² + 6y - 9 = -77
-4y + 16 = -77
-4y = -93
y = -93 / -4
y = 23.25
6. Therefore, the y-coordinate of the point on the y-axis equidistant from (9,5) and (2,3) is 23.25. Hence, the coordinates of the point are (0, 23.25).
In summary, the formula you'll use is the distance formula along with solving the resulting equation to find the coordinates of the point.
I hope this helps!