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Cartesian Plane & Coordinate Axes

What is the a...

Question

What is the area of triangle XYZ, where coordinates of points X, Y and Z are (4, 5), (-1, -6) and (-4, -5) respectively?

19 Square units

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29 Square units

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38 Square units

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58 Square units

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Solution

The correct option is A
19 Square units
Area of $Δ X Y Z$
$= \frac{1}{2} ∣ ∣ ∣ ∣ ∣ \begin{matrix} 4 (- 6) - (- 5) + (- 1) ((- 5) - 5) + (- 4) (5 - (- 6)) \end{matrix} ∣ ∣ ∣ ∣ ∣ = \frac{1}{2} | 4 (- 1) + (- 1) (- 10) + (- 4) (11) | = \frac{1}{2} | - 4 + 10 - 44 | = \frac{1}{2} | - 38 | = \frac{38}{2} = 19 s q . u n i t s$

So, Option (a) is correct.

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Similar questions

Q. The coordinates of points

A, B, C

and

P

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(2, 3), (1, 2), (4, 3)

and

(t, t^{2})

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t > 0

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If the coordinates of two points A and B are (3, 4) and (5, – 2) respectively. Find the coordinates of any point P, if PA = PB and area of $△$ PAB = 10

Q. The coordinates of points

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(2, 3), (1, 2), (4, 3)

and

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is twice the area of

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are two points and P is a point such that PA

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square unit, what are the coordinates of P?

Find the areas of the triangles the whose coordinates of the points are respectively.

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What is the area of triangle XYZ, where coordinates of points X, Y and Z are (4, 5), (-1, -6) and (-4, -5) respectively?

The correct option is A 19 Square unitsArea of ΔXYZ =12∣∣ ∣ ∣∣4(−6)−(−5)+(−1)((−5)−5)+(−4)(5−(−6))∣∣ ∣ ∣∣=12|4(−1)+(−1)(−10)+(−4)(11)|=12|−4+10−44|=12|−38|=382=19 sq.units So, Option (a) is correct.