What does it mean when det[x₁, y₁, 1; x₂, y₂, 1; x₃, y₃, 1] = 0?

Determinants, Adjoint & Inverse · Question 29 of 87

Question 29

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What does it mean when $\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix} = 0$ ?

The three points form a right-angled triangle.Correct answerYour answerThe triangle has area 1 square unit.Correct answerYour answerOne of the points is the origin.Correct answerYour answerThe three points lie on one straight line.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Half the size of this determinant is the area of the triangle with these vertices.
Area 0 means there is no triangle: the points are collinear.

Concept: What a zero determinant means
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsArea of a triangle

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What does it mean when ∣x1y11x2y21x3y31∣=0\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix} = 0​x1​x2​x3​​y1​y2​y3​​111​​=0?

Explanation

What does it mean when $\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix} = 0$ ?