Mathematics

Grade6

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:

### We are given coordinates of some figure. We have to find which geometrical figure, the given points represent. We can do that by finding the length of the sides using the coordinates. Once we find the lengths, we can try to find the possible shapes the given coordinates represent.

## The correct answer is: Square

### 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 sides

To 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

= 21

Side 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|

= 21

Side 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|

= 21

Side 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|

= 21

We 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.