Respuesta :
The required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.
How to estimate the slope of the line?
First, we must obtain the slope of the line perpendicular to BC
Given the coordinates B(7,5), and C(2,3)
Get the slope BC, exists
[tex]$m_{BC} = \frac{3-5}{2-7}[/tex]
= -2/-5 = 2/5
The slope of the line perpendicular to BC will be -5/2.
The slope of the required line in point-slope form exists expressed as;
[tex]$y - y_0 = m(x - x_0)[/tex]
m = -5/2
[tex](x_0, y_0) = (3, 8)[/tex]
Substitute the values into the formula we get
y - 8 = (-5/2)(x - 3)
2(y - 8) = (-5)(x - 3)
2y - 16 = (-5x + 15)
2y + 5x = 15 + 16
2y + 5x = 31
Therefore the required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.
To learn more about the slope of the line refer to:
https://brainly.com/question/19466805
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