Exercise 7.3: Area of a Triangle
Calculate the area of a triangle given three vertices using the coordinate formula. Also check if three points are collinear (area = 0).
Extra Practice Questions
These questions cover the same concepts as Exercise 7.3. Try solving them to build confidence before or after the textbook exercise.
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 $A(2, 3)$, $B(4, -1)$, $C(1, 2)$. Find the length of the median from $A$.
Find the area of the quadrilateral with vertices $(1, 1)$, $(7, -3)$, $(12, 2)$, and $(7, 21)$ by dividing into two triangles.
Find the centroid of a triangle with vertices $(0, 0)$, $(6, 0)$, and $(0, 9)$.
A point $P$ divides the line segment joining $A(1, -5)$ and $B(-4, 5)$ externally in ratio $2:3$. Find the coordinates of $P$.
Find the area of the triangle with vertices $(1, 2)$, $(4, 6)$, and $(5, 2)$.
Find the distance between $(1, 1)$ and $(4, 5)$.
Find the point on the x-axis equidistant from $(5, 4)$ and $(-2, 3)$.
Find the point on the y-axis equidistant from $(-5, -2)$ and $(3, 2)$.
Determine if the points $A(1, 2)$, $B(5, 4)$, $C(3, 8)$, and $D(-1, 6)$ form a square.
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Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Errors in the determinant-style formula expansion
- ✗Forgetting the ½ multiplier
- ✗Getting a negative area (take absolute value)
Other Exercises in Chapter 7
Frequently Asked Questions
How do you find area of a triangle using coordinates?
Area = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|. If this equals 0, the points are collinear.
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