Advertisements
Advertisements
प्रश्न
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
Advertisements
उत्तर
To find the type of triangle, first we determine the length of all three sides and see whatever condition of triangle is satisfy by these sides.
Now, using distance formula between two points,
AB = `sqrt((-4 + 5)^2 + (-2 - 6)^2` ...`[∵ d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)]`
= `sqrt((1)^2 + (-8)^2`
= `sqrt(1 + 64)`
= `sqrt(65)`
BC = `sqrt((7 + 4)^2 + (5 + 2)^2`
= `sqrt((11)^2 + (7)^2`
= `sqrt(121 + 49)`
= `sqrt(170)`
And CA = `sqrt((-5 - 7)^2 + (6 - 5)^2`
= `sqrt((-12)^2 + (1)^2`
= `sqrt(144 + 1)`
= `sqrt(145)`
We see that,
AB ≠ BC ≠ CA
And not hold the condition of Pythagoras in a ΔABC.
i.e., (Hypotenuse)2 = (Base)2 + (Perpendicular)2
Hence, the required triangle is scalene because all of its sides are not equal i.e., different to each other.
APPEARS IN
संबंधित प्रश्न
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Find the distance of a point P(x, y) from the origin.
Find the distance between the points
P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)
Find the distance of the following points from the origin:
(ii) B(-5,5)
Find all possible values of x for which the distance between the points
A(x,-1) and B(5,3) is 5 units.
Find the distance between the following pairs of point.
W `((- 7)/2 , 4)`, X (11, 4)
Find the distances between the following point.
P(–6, –3), Q(–1, 9)
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Find the distance between the following point :
(sec θ , tan θ) and (- tan θ , sec θ)
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
Find the distance between the origin and the point:
(-8, 6)
If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.
Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.
