Answer:
[tex]A=14.5\ units^2[/tex]
Step-by-step explanation:
we know that
The area of the right triangle ABC is equal to
[tex]A=\frac{1}{2}(AB)(BC)[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(10, 7), B(5, 9), and C(3, 4)
step 1
Find the distance AB
A(10, 7), B(5, 9)
substitute in the formula
[tex]d=\sqrt{(9-7)^{2}+(5-10)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(-5)^{2}}[/tex]
[tex]d_A_B=\sqrt{29}\ unjts[/tex]
step 2
Find the distance BC
B(5, 9),C(3, 4)
substitute in the formula
[tex]d=\sqrt{(4-9)^{2}+(3-5)^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2}+(-2)^{2}}[/tex]
[tex]d_B_C=\sqrt{29}\ unjts[/tex]
step 3
Find the area
substitute the values
[tex]A=\frac{1}{2}(\sqrt{29})(\sqrt{29})[/tex]
[tex]A=14.5\ units^2[/tex]
