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 Ic of the centroid of a triangle can be found using the formula zitzeta me= , where 11, 12, 13 are the z-coordinates of the vertices of the triangle. Corresponding formula can be applied for the y-coordinate, too. y V (8,5) (2,4) (6,3) (3.2) (1.0) 10) If Veeru and Dhanno follow the path DV then what will tan be, ife is the angle which DV makes with the horizontal? 1 point 11) If Veeru can run two units per minute and Dhanno can run three units per minute and they meet at a point Mon line segment DV what will be the ordinate (y-coordinate) of M?
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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