Answer:
The coordinates of the point in question is (1, 3).
Step-by-step explanation:
Point (-1, 7) is above and to the left of the point (4, -3). The point in question is to the right and below the point (-1, 7).
What will be the horizontal distance between the point (-1, 7) and the point in question?
The horizontal distance between the point (-1, 7) and (4, -3) is 5. Let the horizontal distance between the point (-1, 7) and the point in question be [tex]a[/tex]. Let the horizontal distance between the point in question and point (4, -3) be [tex]b[/tex].
[tex]\displaystyle \frac{a}{b} = \frac{2}{3}[/tex].
[tex]\displaystyle a = \frac{2}{3} \; b[/tex].
[tex]\displaystyle b = \frac{3}{2}\; a[/tex].
However,
[tex]a + b = 5[/tex].
[tex]\displaystyle a + \frac{3}{2}\; a = 5[/tex].
[tex]\displaystyle \frac{5}{2}\; x= 5[/tex].
[tex]a = 2[/tex].
In other words, the point in question is 2 units to the right of the point (-1, 7). The x-coordinate of this point shall be [tex]-1 + 2 = 1[/tex].
The vertical distance between the point (-1, 7) and the point (4, -3) is 10. Similarly, the point in question is [tex](2/5) \times 10 = 4[/tex] units below the point (-1, 7). The y-coordinate of this point will be [tex]7 - 4 = 3[/tex].
Thus, the point in question is (1, 3).
Answer:
To solve our given problem we will use section formula :]
Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{m. {x}_{2} +n. {x}_{1} }{m + n} ,y= \frac{m. {y}_{2} +n. {y}_{1} }{m + n} \bigg \rgroup \\ \\ \\ [/tex]
Let
(-1 , 7) = (x₁ , y₁)
(4 , -3) = (x₂ , y₂)
m = 2
n = 3
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{2 \times 4 +3 \times - 1 }{2 + 3} ,y= \frac{2 \times - 3 +3 \times 7}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{8 - 3 }{2 + 3} ,y= \frac{ - 6 +21}{2 + 3} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = \frac{5 }{5} ,y= \frac{15}{5} \bigg \rgroup \\ \\ \\ [/tex]
[tex]\tiny: \implies (x,y) = \bigg \lgroup x = 1,y= 3 \bigg \rgroup \\ \\ [/tex]
