Find the area of triangle formed by points A(1,-2), B(2,3) and C(-4,-3). Also find the length of altitude from C(-4,-3) on side AB.
Answers
Answer:
Given information is :
ABCD is a parallelogram
A (1,-2), B (2,3), C(-3.2), D(-4,-3)
AB is the base
Next we find out the equation of line AB.
According to two points formula, equation of a line passing through two points (x1,y1) and (x2,y2) is
y−y2=y1−y2x1−x2(x−x2)
Therefore taking the points (1,-2) and (2,3), equation of AB is
y−3=(−2−3)1−2(x−2)
⟹y−3=−5−1(x−2)
⟹y−3=5(x−2)
⟹y−3=5x−10
⟹5x−y−7=0
From the figure, we can see that the height of the parallelogram is the perpendicular distance of point C from line AB.
Distance (d) of a point (x1,y1) from a line ax+by+c=0 is given by the formula
d=|ax1+by1+c|a2+b2√
Here, (x1,y1)isC(−2,3),a=5,b=−1,c=−7
Hence height,h=|5(−3)−1(2)−7|52+(−1)2√
⟹h=|−15−2−7|25+1√
⟹h=|−24|26√
⟹h=2426√
Rationalising, we get
⟹h=2426√26
⟹h=121326−−√
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Answer:
Step-by-step explanation:
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