pleasehelpmeimbadatmath
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- Oct 22, 2017
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Question: Triangle ABC has vertices A(-1, 4), B(-1, -2) and C(5, 1). The altitude from vertex A meets BC at point D. Determine the area of triangle ABC.
Step 1. I found the slope of BC: y2-y1/x2-x1 = 1+2/5+1 = 3/6 = 1/2 So slope of AD must be -2 because opposite/negative reciprocal.
Step 2. I plugged in the slope of AD and point A into y=mx+b formula: y=mx+b 4=-2(-1)+b 4=2+b 4-2=b 2=b So equation of line AD(Altitude) is y=-2x+2
Step 3. Find the length of line AD to get the area of the triangle: This is where I'm stuck, as I don't know how to get point D's coordinates in order to use the length formula I was taught
[FONT=KaTeX_Main]d =[/FONT][FONT=KaTeX_Main][FONT=KaTeX_Size1]√[/FONT][/FONT][FONT=KaTeX_Main][/FONT][FONT=KaTeX_Main](x[/FONT][FONT=KaTeX_Main]2[/FONT][FONT=KaTeX_Main]−x[/FONT][FONT=KaTeX_Main]1[/FONT][FONT=KaTeX_Main])2[/FONT][FONT=KaTeX_Main]+[/FONT][FONT=KaTeX_Main, Times New Roman, serif](y[/FONT][FONT=KaTeX_Main]2[/FONT][FONT=KaTeX_Main]−y[/FONT][FONT=KaTeX_Main]1[/FONT][FONT=KaTeX_Main])2[/FONT][FONT=KaTeX_Main][/FONT][FONT=KaTeX_Main][/FONT][FONT=KaTeX_Main][/FONT]
Step 1. I found the slope of BC: y2-y1/x2-x1 = 1+2/5+1 = 3/6 = 1/2 So slope of AD must be -2 because opposite/negative reciprocal.
Step 2. I plugged in the slope of AD and point A into y=mx+b formula: y=mx+b 4=-2(-1)+b 4=2+b 4-2=b 2=b So equation of line AD(Altitude) is y=-2x+2
Step 3. Find the length of line AD to get the area of the triangle: This is where I'm stuck, as I don't know how to get point D's coordinates in order to use the length formula I was taught
[FONT=KaTeX_Main]d =[/FONT][FONT=KaTeX_Main][FONT=KaTeX_Size1]√[/FONT][/FONT][FONT=KaTeX_Main][/FONT][FONT=KaTeX_Main](x[/FONT][FONT=KaTeX_Main]2[/FONT][FONT=KaTeX_Main]−x[/FONT][FONT=KaTeX_Main]1[/FONT][FONT=KaTeX_Main])2[/FONT][FONT=KaTeX_Main]+[/FONT][FONT=KaTeX_Main, Times New Roman, serif](y[/FONT][FONT=KaTeX_Main]2[/FONT][FONT=KaTeX_Main]−y[/FONT][FONT=KaTeX_Main]1[/FONT][FONT=KaTeX_Main])2[/FONT][FONT=KaTeX_Main][/FONT][FONT=KaTeX_Main][/FONT][FONT=KaTeX_Main][/FONT]
