coordinate geometry, class 10

Front

What is the perpendicular distance of a point from the x-axis?

Back

The perpendicular distance of a point (x, y) from the x-axis is the absolute value of the y-coordinate, |y|.

Front

Where does the point (0, -11) lie on the coordinate plane?

Back

The point (0, -11) lies on the negative y-axis.

Front

What is the mirror image of a point (x, y) on the x-axis?

Back

The mirror image of the point (x, y) on the x-axis is (x, -y).

Front

How do you calculate the distance between two points J(x1, y1) and K(x2, y2)?

Back

The distance between two points J and K is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What are the coordinates of the origin in a coordinate plane?

Back

The coordinates of the origin are (0, 0).

Front

What is the significance of the x-axis and y-axis in coordinate geometry?

Back

The x-axis is the horizontal line where y=0, and the y-axis is the vertical line where x=0. They intersect at the origin.

Front

How do you determine in which quadrant a point (x, y) lies?

Back

A point (x, y) lies in: 1st Quadrant if x > 0 and y > 0, 2nd Quadrant if x < 0 and y > 0, 3rd Quadrant if x < 0 and y < 0, 4th Quadrant if x > 0 and y < 0.

Front

What is the distance between the points (3, 4) and (3, -2)?

Back

The distance is 6 units.

Front

What is the slope of a line passing through points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).