Q. 285.0( 2 Votes )

# Find the area of the triangle PQR with Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2).

Answer :

Let the co-ordinates of P and R be (a,b) and (c,d) and coordinates of Q are (3, 2)

By midpoint formula.

x = , y =

(2 , - 1) is the mid-point of PQ.

∴ 2 = and -1 =

∴ a = 1 and b = -4

∴ Coordinates of P are (1, -4)

(1 , 2) is the mid-point of QR.

∴ 1 = and 2 =

∴ c = -1 and d = 2

∴ Coordinates of P are (-1, 2)

Area of the triangle having vertices (x_{1},y_{1}), (x_{2},y_{2}) and (x_{3},y_{3})

= |x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})|

Area of ∆PQR = | 3( − 4 – 2 ) + 2( − 1 – 1) + 1( 2 − 4) |

= | − 18 − 4 − 2 |

= 12 sq. units

Hence the area of ∆PQR is 12 sq. units

Rate this question :

If A (-3, 5), B (-2,-7), C (1,-8) and D (6, 3) are the vertices of a quadrilateral ABCD, find its area.

RD Sharma - MathematicsFind the value of k, if the points A (8, 1), B (3, - 4) and C (2, k) are collinear.

RD Sharma - MathematicsFind the value of k if points (k, 3), (6, - 2) and (-3, 4) are collinear.

RD Sharma - MathematicsFind the area of the triangle PQR with Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2).

RD Sharma - MathematicsIf P (-5, - 3), Q (-4, -6), R (2,-3) and S (1, 2) are the vertices of a quadrilateral PQRS, find its area.

RD Sharma - MathematicsIf three points (x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}) lie on the same line, prove that

Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B (2 + , 5) and C(2, 6).

RD Sharma - MathematicsIf the points A (-1,-4), B (b,c) and C (5,-1) are collinear and 2b + c = 4, find the values of b and c.

RD Sharma - Mathematics