1. The coordinates of the point that partitions the directed line segment JK in a 3:2 ratio is (3.2,13.4). 2.The midpoint is (1/2 , -1). 3. length of the image of the line segment after a dilation with a scale factor of 5/2 is 12.5 units.
The length of the image after a dilation will be the original length times the scale factor.
Given :Point J is located at (2,5) and point K is located at (4,19).
Partitions the directed line segment JK in a 3:2 ratio.
1. First, determine the horizontal distance that 4 - 2 = 2
Then divide the horizontal distance by 5.
= 2/5
Now, we have to multiply the above expression by 3 and then add the x coordinate of point J.
= 2/3 x 3 + 2
= 3.2
The y-coordinate of the point is given by
19 - 5 = 14
Then divide the vertical distance by 5.
= 14/5
Now, we have to multiply the above expression by 3 and then add the y coordinate of point J.
= 14/5 x 3 + 5
= 13.4
Hence, the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio is (3.2,13.4)
2.The midpoint is (1/2 , -1).
3. The original length is 5 units.
The new length or the image will be;
(5 units)(5/2)
= 25/2 units
= 12 1/2 units
= 12.5 units
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