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Please help with solving Trigonometry

Hi. I cant solve this problem.

Find d if the line passing through (−2,−1) and (3,2) is perpendicular to the line
dx +2y−3=0.

A (−2,−1) and B(3,2) , line dx +2y−3=0
(gradient AB)*(gradient of the line) = -1

Could you please explain how to do this?

Thank you so much!

Reply 1

Josef314

A (−2,−1) and B(3,2)
-2 = x1
-1 = y1
3= x2
2=y2

To find M, the gradient, you use:
m=y2-y1/x2-x1
so:= 2+1/3+2
=3/5 (you got M using the values from the given coordinates)

Then to find the equation, after finding M, you use this formula:
y-y1=m(x-x1)
so:
y+1=3/5(x-2)y+1
=3/5x -1.4y
y=3/5x -2.4
The perpendicular would be -5/3x(so d would be [-5/3])(Multiply by -1 and then flip the fraction find the reciprocal))
To finally check multiply the two gradients together, it should as the question said give you -1.3/5*-5/3 = -1, so it’s correct