Question

If the vertices of a triangle are (1, –3),(4, p) and (–9, 7) and its area is 15 sq units, find the value of p.

Answer 1

Coordinate geometry is the branch of mathematics which deals with the position of an object lying in a plane.

Each  point in cartesian plane has two coordinates X coordinate and Y coordinate.
The X co-ordinate is called the abscissa.
The Y co-ordinate is called the ordinate.

Coordinates X and Y taken together are called coordinates of a point. (x,y) is called an ordered pair.

SOLUTION:

Area  of the  triangle with  vertices (x1, y1),  (x2, y2) and (x3, y3)  is given by:
1 / 2 [x1(y2 - y3) +  x2 (y3 - y1) + x3 (y1 - y2)]sq.  units.

GIVEN: vertices of a triangle are (1, -3), (4, p) and  (-9, 7)
Here, (x1= 1, y1 = -3),  (x2= 4, y2= p) and (x3= -9 , y3= 7)

Area of ∆ = 15 sq.units
15 = (1/2) × [1(p - 7) + 4(7 + 3) - 9(-3 - p)]

[Area of ∆ = 1 / 2 [x1(y2 - y3) +  x2 (y3 - y1) + x3 (y1 - y2)]]

15 × 2= 1(p - 7) + 4(7 + 3) - 9(-3 - p)
30 =  p - 7 + 4 × 10 + 27 + 9p
30 = p +9p -7 +40 +27
30 =  10p +33 + 27
30 =  10p +60
10p + 60 = 30
10p = 30 - 60
10p = -30
p = -30/10
p = -3
Hence, the value of p is -3

HOPE THIS WILL HELP YOU....

Answer 2

Hey!

Given vertices of triangle are (1, -3), (4, p) and (-9, 7)

and area of triangle is 15sq. units

to find the value of p

(1/2) * [1(p - 7) + 4(7 + 3) - 9(-3 - p)] = 15

1(p - 7) + 4(7 + 3) - 9(-3 - p) = 15 * 2

p - 7 + 4 * 10 + 27 + 9p = 30

10p - 7 + 40 + 27 = 30

10p - 7 + 67 = 30

10p + 60 = 30

10p = 30 - 60


10p = -30

p=-30/10


Therefore, The Value of p is -3

Hope It Helps.☺️