Respuesta :
Answer:
(–6, 10)
Step-by-step explanation:
Because the line is perpendicular its slope is the negative reciprocal of line FG. If we examine the graph and plot out the slope we see that it crosses point (–6, 10).
The slope of a line perpendicular to line FG can be found by changing the
sign and inverting the value of the slope of the line FG.
The point on the perpendicular line passing through point H is [tex]\underline{(-6, \ -10)}[/tex]
Reasons:
The given points on the line FG are; (-8, -8), (8, 4), and H(6, -6)
Required:
The point on the perpendicular line passing through point H and is
perpendicular to FG.
Solution:
The slope of a line, perpendicular to another line that has a slope m, is [tex]-\dfrac{1}{m}[/tex]
The slope, m, of the line FG is found as follows;
[tex]Slope, \, m =\dfrac{4-(-8)}{8-(-8)} = \dfrac{12}{16} = \dfrac{3}{4}[/tex]
Therefore, the slope of the perpendicular line is [tex]-\dfrac{4}{3}[/tex]
The numerator and the denominator of the perpendicular line have the
different signs, therefore, by checking point (-6, -10), we have;
[tex]Slope =\dfrac{10-(-6)}{-6-6} = -\dfrac{16}{12} = -\dfrac{4}{3}[/tex]
Therefore;
The point on the perpendicular line passing through point H is [tex]\underline{(-6, \ -10)}[/tex]
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