Answer:
Explanation:
The line segment joining two points P and Q can be represented by the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line, we need to find the slope, which can be calculated using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points P and Q, respectively.
In this case, the coordinates are:
P = (-3, 2) and Q = (5, 7)
So, the slope is:
m = (7 - 2) / (5 - (-3)) = 5 / 8
Next, we can use either of the points to find the y-intercept. Let's use point P:
b = y - mx, where y and x are the y and x coordinate of the point, respectively.
In this case,
b = 2 - m * (-3) = 2 - (5/8) * (-3) = 2 + 15/8 = 89/8
So, the equation of the line joining the points P and Q is:
y = (5/8)x + 89/8
Now, to find the point where the line crosses the y-axis, we need to find the x-coordinate of the point where y = 0.
So, we have:
0 = (5/8)x + 89/8
Solving for x, we get:
x = -(89/8) / (5/8) = -89 / 5
This means that the line crosses the y-axis at the point (-89/5, 0). To find the ratio in which the line segment is divided by the y-axis, we need to find the ratio of the distance from the y-axis to point P to the distance from the y-axis to point Q.
Let's call the point of intersection with the y-axis R. The distances are then:
PR = (3, 2) and QR = (5 - (-89/5), 7)
The ratio of the distances is then:
PR / QR = (3, 2) / (5 - (-89/5), 7) = 3 / (5 + 89/5) = 3 / (94/5) = 15/47
So, the line segment joining the points P and Q is divided by the y-axis in the ratio 15:47.