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2 answers:
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Answer:
a. The slope of a line parallel to the given line is 1
b. A point on the line parallel to the given line, passing through (−4, 2), is (1,7)
c. The slope of the line perpendicular to the given line is -1
d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)
Step-by-step explanation:
The equation of the line in Slope-intercept form is:
Where m is the slope and b is the y-intercept.
a. For the line
You can identify that:
By definition, two lines are parallel if they have the same slope. Then, the slope of a line parallel to the given line is:
b. The equation of the line in Point-slope form is:
Where m is the slope and () is a point of the line.
Given the point (-4,2), substitute this point and the slope of the line into the equation:
Give a value to "x", substitute it into this equation and solve for "y":
For :
Then, you get the point (1,7)
c. The slopes of perpendicular lines are negative reciprocals, then the slope of a line perpendicular to the given line is:
d. Given the point (-4,2), substitute this point and the slope of the line into the equation:
Give a value to "x", substitute it into this equation and solve for "y":
For :
Then, you get the point (3,-5)
Answer:
Step-by-step explanation:
a). Ratio of OP and RT =
=
=
b). Since ΔOPQ ~ ΔRTS, their corresponding sides will be proportional.
OQ =
OQ = 15 cm
c). m∠P = m∠T = 60°
d). m∠Q = m∠S
By applying angle sum theorem in ΔRST,
m∠R + m∠S + m∠T = 180°
26° + m∠S + 60° = 180°
m∠S = 180° - 86°
= 94°
Therefore, m∠Q = m∠S = 94°
