1.what is the length of the segment joining 3,6 and -2,-6 : 13 units
2.what is the center of the circle (x+6)^2+(y-8)^2=144 => (-6,8)
3.what is the slope of the line 3y+2x-6=0=> -2/3
1.what is the length of the segment joining (3,6) and (-2,-6)?
(x1,y1) = (3,6)
(x2,y2) = (-2,-6)
The length of a segment is given by:
2.what is the center of the circle (x+6)^2+(y-8)^2=144
The equation of circle is given by:
Here, h and k are the coordinates of centre of circle
x - h = x+6
-h = 6
h = -6
y - 8 = y - k
-8 = - k
k = 8
The center of circle is: (-6,8)
3.what is the slope of the line 3y+2x-6=0
We have to convert the equation in slope-intercept form to find the slope
Slope-intercept form is:
y = mx+b
Dividing both sides by 3
In slope-intercept form, the co-efficient of x is the slope of the line so
m = -2/3
Keywords: Coordinate geometry, Slope
Learn more about coordinate geometry at:
1. Find the equation of the parabola
The vertex is at (0, 0), so the axis of symmetry is the y-axis.
The graph passes through (7, 7), so it must also pass through (-7,7).
The vertex form of the equation for a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
If the vertex is at (0, 0),
h = 0 and k = 0
The equation is
y = ax²
2. Find the value of a
Insert the point (7,7).
7 = a(7)²
1 = 7a
a = ⅐
The equation in vertex form is
y = ⅐x²
3. Calculate the length of the segment when y = 6
The distance between the two points is the length (l) of line AB.
A is at (√42, 6); B is at (-√42, 6).
l = x₂ - x₁ = √42 – (-√42) = √42 + √42 = 2√42 ≈ 2 × 6.481 ≈ 13.0
For this case we must find the distance between the points:
By definition, the distance between two points is found by:
Substituting the points:
So the distance is 13 units
The length of the segment is 6.63 inches
Given that the radius of the circle is 12 inches.
The center of the circle to the endpoint and the midpoint of the chord forms a right angled triangle.
The hypotenuse is 12 inches.
One of the sides is
Applying the Pythagorean theorem, we have,
Thus, we have,
Simplifying, we get,
Taking square root on both sides of the equation, we have,
Thus, the length of the line segment is 6.63 inches.
x² + 10² = 12²
The value of x is approximately equal to 6.63 in.
d≈8.9 units (to the nearest tenth of a unit)
1. length of the segment = 5 units
2. length of the segment = 9.22 units
To find the length of a segment joining two points (x,y) and (x',y') we always use the formula
Distance between the points = √(x-x')²+(y-y')²
In our question the given points are (-1,6) and (-5,3) the distance between them will be = √(-1+5)²+(6-3)² = √4²+3² = √16+9 =√25 = 5 Units
2. Length between the points (-4,1) and (3,7) will be = √(-4-3)²+(1-7)²
= √(-7)²+(-6)² = √49+36 = √85 = 9.22 units