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The coordinate axes (x and yaxis) divide the plane, in how many quadrants?
xaxis and yaxis divide the plane in 4 quadrants.
The ordinate of any point on xaxis will be
Every point on xaxis is of the form (x, 0)
∴ ordinate of any point on xaxis = 0
If the abscissa of a point is negative. The point will lie in
Sign convention for Quadrants are
I^{st} quadrant → (+, +)
II^{nd} quadrant → (, +)
III^{rd} quadrant → (, )
IV^{th} quadrant → (+, )
∴ Required point will lie in II or III quadrant.
If a circle is such that xaxis is tangent to it, if the coordinate of centre of circle is (2, 3), then the point of tangency will have ordinate equal to
O is the centre of circle and A is the point of tangency.
∵ Point of tangency lies on x axis
∴ Ordinate of point = 0
The perpendicular distance of point (11, 2) from yaxis will be:
Perpendicular distance from yaxis
= abscissa = 11 = 11
A point on line y = 3x + 2 has equal ordinate and abscissa, then the point will lie in
If abscissa = ordinate, i.e, x = y then using this relation in equation of line, we have
x = 3x + 2 ⇒ x = 1
∴ Point has coordinates = (1, 1)
Point has sign convection of (, )
∴ Point will lie in 3^{rd} quadrant
Area of PQR = 1/2 × PQ × QR
= 1/2 × 4 × 3 = 6 (units)^{2}
A (2, 3), B (3, 0) and C (14, 13) are vertices of triangle ABC. Then, the centroid of triangle will lie in:
∵ Centroid of any D lies within it, and all the coordinates A, B and C are in I^{st }quadrant (Positive)
∴ centroid will lie in I^{st }quadrant.
The mirror image of point (4, 3) about xaxis will be
Point A is 3 units above xaxis.
∴ Its mirror image will be 3 units below xaxis, and the xcoordinate will remain constant
∴ Coordinates of point B ≡ (4, 3)
A point P on line 2x + 3y = 5, has equal value of both ordinate and abscissa, then the mirror image of point P about yaxis will be:
When ordinate = abscissa, then y = x
∴ 2x + 3x = 5
⇒ 5x = 5
⇒ x = 1
∴ x = y = 1 will be point on line having equal abscissa and ordinate
∴ Point P = (1, 1)
∴ Its image about yaxis will be (1, 1).
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