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Coordinate Geometry

Multiple Choice Questions

What would be the equation of the line, which intercepts x-axis at -5 and perpendicular to the line y = 2x - 3?

x - 2y = -5
x + 2y = 5
x + 2y = -5
x - 2y = 5

The area of the triangle formed by the graphs of the equations x = 4, y = 3 and 3x + 4y = 12 is

4 sq units
12 sq units
6 sq units
6 sq units

594 Views

The coordinates of the vertices of a right angled triangle are P(3, 4), Q(7, 4) and R(3, 8), the right angle being at P. The coordinates of the orthocentre of $increment PQR$ are

(3, 4)
(7, 4)
(3, 8)
(3, 8)

588 Views

The area (in square units) of the triangle formed by the graphs of the equations x = 4, y = 3 and 3x + 4y = 12 is

746 Views

If the ordinate and abscissa of the point (k, 2k -1) be equal, then the value of k is

0
-1
1
1

578 Views

Area of the triangle formed by the graph of the straight lines x - y = 0, x + y = 2 and x-axis is

1 sq unit
2 sq units
1 sq units
None of these

585 Views

7.
The graphs of x + 2y = 3 and 3x - 2y = 1 meet the Y-axis at two points having distance

$8 over 3 space units$
$4 over 3 units$

1 unit

1 unit

1 unit

On Y-axis, x = 0
Now, put x = 0 in x + 2y = 3
$2 straight y space equals space 3 space space rightwards double arrow space space straight y space equals space 3 over 2$
Putting x = 0 in 3x - 2y = 1,
$negative 2 straight y space equals space 1 space space rightwards double arrow space space straight y space equals space minus 1 half$
∴ Points on Y-axis are
$open parentheses 0 comma space 3 over 2 close parentheses space space and space space open parentheses 0 comma space space minus 1 half close parentheses.$
∴ Required distance
$equals space square root of left parenthesis 0 minus 0 right parenthesis squared plus space open parentheses 3 over 2 plus 1 half close parentheses squared end root space equals space square root of 0 plus 4 end root space equals space 2 space units$