Question

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,
a)If Veeru and Dhanno follow the path
D
V
then what will
t
a
n
θ
be, if
θ
is the angle which
D
V
makes with the horizontal?

(Answer should be till two decimal places, use zero before the decimal if value is less than one)​

Answer 1

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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