The line segment joining the points (3 -1) and (-6 5) is trisected . T...
Which one of the following materials cannot be used make a lens?
A. water
B. glass
C. acrylic
D. clay
The line segment joining the points (3 -1) and (-6 5) is trisected . T...
Given information:
We are given the coordinates of two points, A(3, -1) and B(-6, 5), and we need to find the coordinates of the point of trisection on the line segment joining A and B.
Approach:
To find the point of trisection on the line segment AB, we can use the concept of the section formula. According to the section formula, the coordinates of a point dividing a line segment into two segments of lengths m:n are given by:
x = (nx1 + mx2) / (m + n)
y = (ny1 + my2) / (m + n)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and m and n are the ratios in which the line segment is divided.
In this case, we need to trisect the line segment, which means dividing it into three equal parts. Therefore, the ratios of the line segment lengths will be 1:1:1.
Calculations:
Let's calculate the coordinates of the point of trisection using the section formula:
x = (1*3 + 1*(-6)) / (1 + 1) = (3 - 6) / 2 = -3/2 = -1.5
y = (1*(-1) + 1*5) / (1 + 1) = (-1 + 5) / 2 = 4/2 = 2
Therefore, the coordinates of the point of trisection are (-1.5, 2).
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