A line PQ with endpoints P(2,1) and Q(7,6)is to be moved by 3 Units in X-direction and 4 Unit in Y- direction. Determine the co-ordinate of the endpoints for the translated line.
Answers
New end points P(5,4) and Q(10,10)
Concept:
The linear displacement of a point from its initial position is known as translation. The horizontal and vertical positions of a point are labeled first and second, respectively, with regard to the origin of an x-y coordinate plane. X-coordinates to the left of the y-axis and y-coordinates below the x-axis are assigned negative values.
Given:
Point P(2,1) and point Q(7,6).
The points moved by 3 units in X-direction and 4 Units in Y-direction.
Find:
The endpoints after translating.
Solution:
Point P = (2,1).
The point is moved by 3 units in X-direction, then endpoint of P = (2+3, 1)
= (5,1).
The point is moved by 4 units in Y-direction, then endpoint of P = (5, 1+4)
= (5,5).
The point is moved by 3 units in X-direction, then endpoint of
Q = (7+3, 6)
= (10,6).
The point is moved by 4 units in Y-direction, then end point of
Q = (10, 6+4)
= (10, 10).
Hence, the final points are P(5, 5) and Q(10,10).