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
x
c
of the centroid of a triangle can be found using the formula
x
c
=
x
1
+
x
2
+
x
3
3
, where
x
1
,
x
2
,
x
3
are the
x
-coordinates of the vertices of the triangle. Corresponding formula can be applied for the
y
-coordinate, too.

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?
1 point
If Veeru can run two units per minute and Dhanno can run three units per minute and they meet at a point M on line segment DV, what will be the ordinate (y-coordinate) of M ?

Answer 1

Answer:

.75

Step-by-step explanation:

centriod of D

(x1+x2+x3)/3 ,(y1+y2+y3)/3

((1+2+3)/3 , (0+4+2)/3

D(2,2)

centroid of V

(x1+x2+x3)/3 , (y1+y2+y

3)/3

(6+4+8)/3 , (3+7+5)/3

V(6,5)

we can get tan(@) by finding slope of D and V

m= tan@=(y2-y1)/(x2-x1)

tan@= (5-2)/(6-2)

tan@=3/4 = 0.75

Answer 2

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

Angle = tan⁻¹ ( 3/4)  =  37°

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