Exercise 7.1: Distance Formula
Find distances between points on the coordinate plane. Check if three points form a triangle, a line, or specific shapes.
Extra Practice Questions
These questions cover the same concepts as Exercise 7.1. Try solving them to build confidence before or after the textbook exercise.
The origin has coordinates:
The coordinates of the point which divides the line segment joining $(1, 3)$ and $(5, 7)$ in the ratio $1:1$ are:
The vertices of a triangle are $(2, 1)$, $(5, 2)$, and $(3, 4)$. Find its centroid.
Find the centroid of a triangle with vertices $(0, 0)$, $(6, 0)$, and $(0, 9)$.
The distance of the point $(5, 12)$ from the origin is:
The vertices of a triangle are $A(2, 3)$, $B(4, -1)$, $C(1, 2)$. Find the length of the median from $A$.
If $A(4, -8)$, $B(3, 6)$, and $C(5, -4)$ are the vertices of a triangle, find the length of the median from $B$.
The section formula gives the coordinates of a point dividing a line segment in ratio $m:n$ as:
The centroid of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ is:
If the point $P(x, y)$ is equidistant from $A(7, 1)$ and $B(3, 5)$, find the relation between $x$ and $y$.
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Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Sign errors when subtracting coordinates
- ✗Forgetting to take the square root at the end
- ✗Not squaring negative differences correctly
Other Exercises in Chapter 7
Frequently Asked Questions
What is the distance formula?
The distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂-x₁)² + (y₂-y₁)²].
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