Two points A and B have coordinates (5, 7) and (-1, 3) .
(a) Find the mid-point of the line AB.
(b) Find the length AB to 3 s.f.
(2) Write the coordinates of the points where the line 2y+3x=12 crosses the x-axis and y-axis.?
(a) just find the average of x-values and y-values
(b) d^2 = (-1-5)^2 + (3-7)^2
(c) The line through A and B is y-7 = 2/3 (x-5)
now just solve the system of equations as usual
a. A(5, 7), M(x, y), B(-1, 3).
x-5 = 1/2(-1-5)
X = 2.
y-7 = 1/2(3-7)
Y =
b. AB = sqrt((-1-5)^2 + (3-7)^2)) =
2. 3x+2y = 12.
Y = 0.
3x+2*0 = 12
X =
To find the midpoint of the line AB, you can average the x-coordinates and the y-coordinates of points A and B separately.
(a) Midpoint of AB:
The x-coordinate of the midpoint is the average of the x-coordinates of A and B:
x-coordinate = (5 + (-1)) / 2 = 4 / 2 = 2
The y-coordinate of the midpoint is the average of the y-coordinates of A and B:
y-coordinate = (7 + 3) / 2 = 10 / 2 = 5
So, the midpoint of line AB is (2, 5).
To find the length AB, you can use the distance formula:
(b) Length of AB:
The distance formula is given by:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates of A and B into the distance formula:
distance = √[(-1 - 5)^2 + (3 - 7)^2]
distance = √[(-6)^2 + (-4)^2]
distance = √[36 + 16]
distance = √52
Rounding the result to three significant figures, the length AB is approximately 7.211.
To find the points where the line 2y + 3x = 12 crosses the x-axis and y-axis, you can set either x or y to zero and solve for the other variable.
(2) Points where the line crosses the x-axis and y-axis:
To find the point where the line crosses the x-axis, set y = 0, and solve for x:
2(0) + 3x = 12
0 + 3x = 12
3x = 12
x = 12 / 3
x = 4
So, the line 2y + 3x = 12 crosses the x-axis at the point (4, 0).
To find the point where the line crosses the y-axis, set x = 0, and solve for y:
2y + 3(0) = 12
2y + 0 = 12
2y = 12
y = 12 / 2
y = 6
So, the line 2y + 3x = 12 crosses the y-axis at the point (0, 6).