Veeru (V ) and his horse Dhanno (D) are running towards each other from their locations which are the centroids of two different triangles shown in figure below. The x - coordinate xc of the centroid of a triangle can be found using the formula xc=x1+x2+x33 , where x1,x2,x3 are the x-coordinates of the vertices of the triangle. Corresponding formula can be applied for the y-coordinate, too.
Answers
Given : Veeru (V) and his horse Dhanno (D) are running towards each other from their locations which are the centroids of two
different triangles
viro can run two units per minute and Dhanno can run 3 units per minute and they meet at a point m on line segment DV
To Find : y co-ordinate of m
Solution:
D - x coordinate = (1 + 2 + 3)/3 = 2
D - y coordinate = (0 + 4 + 2)/3 = 2
D = (2 , 2)
V - x coordinate = (6 + 4 + 8)/3 = 6
V - y coordinate =
(3 + 7 + 5)/3 = 5
V = (6 , 5)
Distance between D & V = √(6 - 2)² ( 5 - 2)² = 5 unit
Dhanno run 3 unit per minute and Viru run 2 unit per minutes
Hence Dhanno covers 3 units and Viru 2 units
So point M
Divides DV in 3 : 2 Ratio
M = ( 3 * 6 + 2 * 2)/(3 + 2) , ( 3 * 5 + 2 * 2)/(3 + 2)
= (22/5 , 19/5)
y co-ordinate of m = 19/5
Slope = ( 5 -2 )/(6 - 2) = 3/4 = 0.75
Angle = tan⁻¹ ( 3/4) = 37°
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