Please help! Points E, D, and H are the midpoints of the sides of ΔTUV. UV=48, TV=62, and HD=48. Find HE.
1 answer:
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I'm here to help. Those 3 points all lie on the same line. We know this because if we find the slope between any 2 of those points, it is the same. I'll show you: 
. Now another 2 points: 
. The same holds for the first and third points. So we got that out of the way. Now we will pick any one of those points and use the x and y values and our slope to write an equation of that line and then finally solve for the x and y intercepts. I'm going to use the first point (10, 20): 
. We will simplify to get it into y = mx + b form: 
and 
and finally, 
. The y-intercept exists when x = 0, so when x = 0, y = 36. The x-intercept exists when y = 0, so when y = 0, x = 22.5. In summary, y-intercept: (0, 36). x-intercept: (22.5, 0) and you're all done!
Answer:
Step-by-step explanation:
In similar triangles, the corresponding sides are in same proportion.
Cross multiply,
4x*12 = 15*(3x + 1)
48x = 15*3x + 15*1
48x = 45x + 15
48x -45x = 15
3x = 15
x = 15/3
x = 5