Mathematics
Easy

Question

Identify the geometrical figure whose vertices are at the coordinates, A (4, -10), B (4, 11), C (25, 11), D (25, -10)

Square    Rectangle    Parallelogram    Circle

Hint:

The given points are:A is (4,-10)B is (4,11)C is (25,11)D is (25,-10)We have to find the length of the all sidesTo find the length we will use the following criteria:1) If x coordinate is same, we will find the absolute distance using y coordinate.2) If y coordinate is same we will use the x coordinate to find absolute distance.3) If the points are in same quadrant, we will have to subtract the absolute distances to find length.4) If the points are in adjacent quadrants, we will have to add the absolute distances to find length.Side AB:For this, x coordinate is same. We will use y coordinate. They have different signs.Absolute distance of the point A = |-10|Absolute distance of the point B = |11|Length of AB = |11| + |-10|= 11 + 10= 21Side BC:For this, y coordinate is same. We will use x coordinate. They have same sign.Absolute distance of the point B = |4|Absolute distance of the point C = |25|Length of BC = |25| - |4|= 21Side CD:For this, x coordinate is same. We will use y coordinate. They have different sign.Absolute distance of the point C = |11|Absolute distance of the point D = |-10|Length of CD = |11| + |-10|= 21Side DA:For this, y coordinate is same. We will use x coordinate. They have same sign.Absolute distance of the point D = |25|Absolute distance of the point A = |4|Length of DA = |25| - |4|= 21We can see that the length of all sides is same.A shape with all sides same is square.So, the given points represent a square.

An absolute distance is the length of the point from the respective axis. If x coordinate is same then its length is measured from x axis. It is a positive quantity. We can use distance formula to find the length of sides of rectangle too.