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NCERT · Ganita Manjari · Volume 1 · Chapter 1

Orienting Yourself: The Use of Coordinates

34 videos in this chapter

Understanding coordinates

10 videos

Chapter 1Why Do We Need Coordinates?4:04Why Do We Need Coordinates?You'll learn: Describe an exact location using a reference system and two numbers.Chapter 1How Grid Thinking Developed into Coordinate Geometry4:12How Grid Thinking Developed into Coordinate GeometryYou'll learn: Trace the introduction’s progression from grids and navigation to zero, negative numbers and algebra with geometry.Chapter 1From a Number Line to a Coordinate Plane3:46From a Number Line to a Coordinate PlaneYou'll learn: Explain one-dimensional and two-dimensional location. Show why a plane needs two coordinates.Chapter 1Meet the x-Axis, y-Axis and Origin3:40Meet the x-Axis, y-Axis and OriginYou'll learn: Identify horizontal and vertical axes, perpendicular intersection, origin (0,0) and equal unit marks.Chapter 1Positive and Negative Directions on the Plane3:50Positive and Negative Directions on the PlaneYou'll learn: Connect right/up to positive values and left/down to negative values.Chapter 1What Happens When One Coordinate Is Zero?3:32What Happens When One Coordinate Is Zero?You'll learn: Locate points of the form (x,0), (0,y) and (0,0), including decimal coordinates.Chapter 1What Do the Two Numbers in (x,y) Mean?3:54What Do the Two Numbers in (x,y) Mean?You'll learn: Explain horizontal and vertical positions and perpendicular guides to the axes.Chapter 1Four Quadrants: Finding a Point from Its Signs3:32Four Quadrants: Finding a Point from Its SignsYou'll learn: Explain quadrant numbering and the four sign combinations.Chapter 1Read a Point, Plot a Point—and Check It3:55Read a Point, Plot a Point—and Check ItYou'll learn: Locate points from coordinates and read coordinates from a graph.Chapter 1Does Swapping the Coordinates Change the Point?3:53Does Swapping the Coordinates Change the Point?You'll learn: Explain why ordered pairs depend on order and coincide after swapping only when x=y.

Exploring Reiaan’s room

6 videos

Chapter 1Turn a Room into a Two-Dimensional Map4:02Turn a Room into a Two-Dimensional MapYou'll learn: Explain floor plans, scale and object corners. Identify information a floor plan cannot specify.Chapter 1Use Coordinates to Measure and Compare Doorways4:00Use Coordinates to Measure and Compare DoorwaysYou'll learn: Read endpoints, find doorway widths and compare the room and bathroom doors.Chapter 1Three Table Feet Are Given—Where Is the Fourth?3:48

Distance and reflection

6 videos

Chapter 1Find Distances Along Horizontal and Vertical Lines3:54Find Distances Along Horizontal and Vertical LinesYou'll learn: Recognise equal x- or y-coordinates and use the absolute difference of the other coordinates.Chapter 1Find a Slanting Distance by Building a Right Triangle3:45Find a Slanting Distance by Building a Right TriangleYou'll learn: Turn horizontal and vertical shifts into perpendicular legs and find direct distance.Chapter 1Build the Distance Formula from the Picture4:04

Applications

5 videos

Chapter 1Predict a Shape Before Plotting Its Points3:41Predict a Shape Before Plotting Its PointsYou'll learn: Predict axis-parallel sides, perpendicular sides and mirror points before checking the graph.Chapter 1Build a Right Triangle Around a Given Point3:50Build a Right Triangle Around a Given PointYou'll learn: Construct a valid right triangle using a given vertex and calculate its three sides.Chapter 1Can a Street Address Identify More Than One Crossing?4:14

Challenge explorations

7 videos

Chapter 1Are Three Points on One Straight Line?4:20Are Three Points on One Straight Line?You'll learn: Use distance addition to test collinearity, then plot both sets to verify.Chapter 1Build Isosceles Triangles Using Coordinates4:06Build Isosceles Triangles Using CoordinatesYou'll learn: Construct the two requested triangle types and verify their properties.Chapter 1What Makes a Point the Midpoint?4:28What Makes a Point the Midpoint?

Three Table Feet Are Given—Where Is the Fourth?

You'll learn: Complete an axis-aligned rectangle, find length and width and discuss placement.

Chapter 1Map the Bathroom Using Negative Coordinates4:16Map the Bathroom Using Negative CoordinatesYou'll learn: Read bathroom and shower corners, identify the shower shape and allocate spaces.

Chapter 1Will the Bathroom Door Hit the Wardrobe?4:00Will the Bathroom Door Hit the Wardrobe?You'll learn: Reason about a door’s hinged movement and what changes when it is widened.

Chapter 1Place a Dining Table Exactly in the Centre4:10Place a Dining Table Exactly in the CentreYou'll learn: Extend the room plan, identify dining-room corners and use equal margins for a centred table.

Build the Distance Formula from the Picture

You'll learn: Generalise coordinate differences and derive the square-root distance expression.

Chapter 1Use the Distance Formula to Measure a Triangle3:50Use the Distance Formula to Measure a TriangleYou'll learn: Apply the formula to all three sides and interpret exact square-root lengths.

Chapter 1Why the Distance Formula Works with Negative Coordinates4:02Why the Distance Formula Works with Negative CoordinatesYou'll learn: Subtract negative coordinates and explain why reversing endpoint order preserves distance.

Chapter 1Reflect a Triangle: What Changes and What Stays the Same?3:50Reflect a Triangle: What Changes and What Stays the Same?You'll learn: Track coordinate changes under reflection in either axis and compare side lengths.

Can a Street Address Identify More Than One Crossing?

You'll learn: Test whether a street-index convention identifies a unique crossing and why direction information matters.

Chapter 1Do Two Circular Icons Fit and Overlap on a Screen?4:40Do Two Circular Icons Fit and Overlap on a Screen?You'll learn: Check circle extents against screen boundaries and compare centre distance with the radii.

Chapter 1Is This Tilted Quadrilateral Really a Square?4:12Is This Tilted Quadrilateral Really a Square?You'll learn: Use distances to justify the shape and determine its area.

You'll learn: Check that a midpoint lies on the segment and divides it equally. Discover coordinate averages.

Chapter 1Find a Missing Endpoint from the Midpoint4:12Find a Missing Endpoint from the MidpointYou'll learn: Reverse the coordinate-average relationship to find an unknown endpoint.

Chapter 1Divide a Segment into Three Equal Parts4:00Divide a Segment into Three Equal PartsYou'll learn: Extend equal division from halves to thirds and find both internal division points.

Chapter 1Is a Point Inside, On or Outside a Circle?4:14Is a Point Inside, On or Outside a Circle?You'll learn: Find a common radius from distances to the origin and classify additional points.

Chapter 1Rebuild a Triangle from Its Side Midpoints4:28Rebuild a Triangle from Its Side MidpointsYou'll learn: Combine three midpoint relationships to recover the original triangle vertices.