Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 30
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33Q. No.
Value Points
Marks
Q19. Any point P on x axis is given by (x,0)
½
(Distance) between (x, 0) and (7, 6) is given by œ (x — 7)² + 6² ……(i)
1
(Distance) between (x, 0) and (—3, 4) is given by œ (x + 3)² + 4² ……(ii)
1
2
2
(i) = (ii) Ü x
—14x + 49 + 36 = x
+ 6x + 9 + 16
1
OR, 20x = 60
x=3
∴ The point is (3,0)
½
Q20. Let the point D be (x, y)
∴ mid point of BD =
(
)
(x+1), y
1 ½
2
2
Mid point of AC = (5/2, 1)
1
This is the same point
x+1
5
∴
Ü x=4
=
2
2
y
=1 Ü y = 2
and
½ +½
2
∴ The co-ordinates of D are (4, 2)
½
OR
9
Co-ordinates of D are (
,10)
1
2
∴ The length of AD
9
2
2
œ (4-
=
)
+ (—8 —10)
2
1
1297
œ
œ
=
+ 324
=
1
4
4
1
œ 1297
=
½
2
Co-ordinates of centroid
(
)
= 4 – 9+18 , —8+7+13
1
3
3
13
= (
, 4)
½
3
165
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